![6 1 Understanding the Universe: Cosmology, Astrophysics, Particles…
Fig. 1.2 Presently observed elementary particles. Fermions (the matter particles) are listed in the
first three columns; gauge bosons (the field particles) are listed in the fourth column. The Higgs
boson is standing alone. Adapted from MissMJ [CC BY 3.0 (http://creativecommons.org/licenses/
by/3.0)], via Wikimedia Commons
interactions might be the remnants of one single interaction that would occur at
extreme energies—e.g., the energies typical of the beginning of the Universe. By
increasing order of strength:
1. The gravitational interaction, acting between whatever pair of bodies and domi-
nant at macroscopic scales.
2. The electromagnetic interaction, acting between pairs of electrically charged par-
ticles (i.e., all matter particles, excluding neutrinos).
3. The weak interaction, also affecting all matter particles (with certain selection
rules) and responsible, for instance, for the beta decay and thus for the energy
production in the Sun.
4. The color force, acting among quarks. The strong interaction,7
responsible for
binding the atomic nuclei (it ensures electromagnetic repulsion among protons
7This kind of interaction was first conjectured and named by Isaac Newton at the end of the
seventeenth century: “There are therefore agents in nature able to make the particles of bodies stick
together by very strong attractions. And it is the business of experimental philosophy to find them
out. Now the smallest particles of matter may cohere by the strongest attractions and compose
bigger particles of weaker virtue; and many of these may cohere and compose bigger particles
whose virtue is still weaker, and so on for diverse successions, until the progression ends in the
biggest particles on which the operations in chemistry, and the colors of natural bodies depend.” (I.
Newton, Opticks).](https://image.slidesharecdn.com/16412690-250520150137-b8979776/85/Introduction-To-Particle-And-Astroparticle-Physics-Unknown-38-320.jpg)
![20 1 Understanding the Universe: Cosmology, Astrophysics, Particles…
Fig. 1.10 Energy spectrum
(number of incident particles
per unit of energy, per
second, per unit area, and per
unit of solid angle) of the
primary cosmic rays. The
vertical band on the left
indicates the energy region
in which the emission from
the Sun is supposed to be
dominant; the central band
the region in which most of
the emission is presumably
of galactic origin; the band
on the right the region of
extragalactic origin. By
Sven Lafebre (own work)
[GFDL http://www.gnu.org/
copyleft/fdl.html], via
Wikimedia Commons
this energy is dominated by cosmic rays produced by extragalactic sources, mostly
supermassive black holes growing at the centers of other galaxies. For even higher
energies (more than one million TeV) the cosmic-ray spectrum becomes less steep,
resulting in another change of slope, called the “ankle”; some others believe that
the knee is caused by a propagation effect, and the threshold for the dominance of
extragalactic sources is indeed close to the ankle. Finally, at the highest energies in
the figure a drastic suppression is present—as expected from the interaction of long-
traveling particles with the cosmic microwave background, remnant of the origin of
the Universe.15
The majority of high-energy particles in cosmic rays are protons (hydrogen
nuclei); about 10% are helium nuclei (nuclear physicists usually call them alpha par-
ticles), and 1% are neutrons or nuclei of heavier elements. Together, these account
15A theoretical upper limit on the energy of cosmic rays from distant sources was computed in 1966
by Greisen, Kuzmin, and Zatsepin, and it is called today the GZK cutoff. Protons with energies above
a threshold of about 1020 eV suffer a resonant interaction with the cosmic microwave background
photons to produce pions through the formation of a short-lived particle (resonance) called ∆:
p + γ → ∆ → N + π. This continues until their energy falls below the production threshold.
Because of the mean path associated with the interaction, extragalactic cosmic rays from distances
larger than 50 Mpc from the Earth and with energies greater than this threshold energy should be
strongly suppressed on Earth, and there are no known sources within this distance that could produce
them. A similar effect (nuclear photodisintegration) limits the mean free path for the propagation
of nuclei heavier than the proton.](https://image.slidesharecdn.com/16412690-250520150137-b8979776/85/Introduction-To-Particle-And-Astroparticle-Physics-Unknown-52-320.jpg)
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- 8. Alessandro De Angelis • Mário Pimenta Introduction to Particle and Astroparticle Physics Multimessenger Astronomy and its Particle Physics Foundations Second Edition 123
- 9. Alessandro De Angelis Department of Mathematics, Physics and Computer Science University of Udine Udine Italy and INFN Padova and INAF Padua Italy Mário Pimenta Laboratório de Instrumentação e Física de Partículas, IST University of Lisbon Lisbon Portugal ISSN 2192-4791 ISSN 2192-4805 (electronic) Undergraduate Lecture Notes in Physics ISBN 978-3-319-78180-8 ISBN 978-3-319-78181-5 (eBook) https://doi.org/10.1007/978-3-319-78181-5 Library of Congress Control Number: 2018938359 1st edition: © Springer-Verlag Italia 2015 2nd edition: © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
- 10. Foreword My generation of particle physicists has been incredibly fortunate. The first paper I ever read was George Zweig’s highly speculative CERN preprint on “aces,” now called quarks. After an exhilarating ride, from the chaos of particles and resonances of the sixties to the discovery of the Higgs boson that gives them mass, quarks are now routinely featured in standard physics texts along with the levers and pulleys of the first chapter. My office was one floor below that of Monseigneur Lemaitre; strangely, I only knew of his existence because I used the computer that he had built. That was just before the discovery of the microwave background brought him fame and the juggernaut that is now precision cosmology changed cosmology from boutique science to a discipline pushing the intellectual frontier of physics today. Over the same decades, the focus of particle physics shifted from cosmic rays to accelerators, returning in the disguise of particle astrophysics with the discovery of neutrino mass in the oscillating atmospheric neutrino beam, the first chink in the armor of the Standard Model. This triptych of discoveries represents a masterpiece that is also strikingly incomplete—like a Titian painting, only the details are missing, to borrow Pauli’s description of Heisenberg’s early theory of strong interactions. The mechanism by which the Higgs endows the heaviest quark, the top, with its mass is unstable in the Standard Model. In fact, the nonvanishing neutrino mass directly and unequivocally exposes the incompleteness of the symmetries of the Standard Model of quarks and leptons. Precision cosmology has given birth to a strange Universe of some hydrogen and helium (with traces of the other chemical elements) but mostly dark energy and dark matter. The stars, neutrinos, microwave photons, and supermassive black holes that constitute the rest do not add up to very much. But this is business as usual—deeper insights reveal more fundamental questions whose resolution is more challenging. Their resolution has inspired a plethora of novel and ambitious instrumentation on all fronts. After decades of development on the detectors, we recently inaugurated the era of multimessenger astronomy for both gravitational waves and high-energy neu- trinos. On August 17, 2017, a gravitational wave detected by the LIGO-Virgo v
- 11. interferometers pointed at the merger of a pair of neutron stars that was subse- quently scrutinized by astronomical telescopes in all wavelengths of astronomy, from radio waves to gamma rays. Barely a month later, some of the same instru- ments traced the origin of a IceCube cosmic neutrino of 300 TeV energy to a distant flaring active galaxy. At the close of the nineteenth century, many physicists believed that physics had been essentially settled—we do not live with that illusion today. Yet, the key is still to focus on the unresolved issues, as was the case then. Based on the size of the Sun and given the rate that it must be contracting to transform gravitational energy into its radiation, Lord Kelvin concluded that the Sun cannot be more than 20–40 million years old. His estimate was correct and directly in conflict with known geology. Moreover, it did not leave sufficient time for Darwin’s evolution to run its course. The puzzle was resolved after Becquerel accidentally discovered radioac- tivity, and Rutherford eventually identified nuclear fusion as the source of the Sun’s energy in 1907. The puzzling gap between some ten million and 4.5 billion for the age of the solar system provided the hint of new physics to be discovered at a time when many thought “only the details were missing.” Today we are blessed by an abundance of puzzles covering all aspects of particle physics, including the incompleteness of the Standard Model, the origin of neutrino mass, and the per- plexing nature of dark matter and dark energy. This book will inspire and prepare students for the next adventures. As always, the science will proceed with detours, dead ends, false alarms, missed opportunities, and unexpected surprises, but the journey will be exhilarating and progress is guaranteed, as before. Francis Halzen Francis Halzen is the principal investigator of the IceCube project, and Hilldale and Gregory Breit Professor in the department of physics at the University of Wisconsin–Madison. vi Foreword
- 12. Preface This book introduces particle physics, astrophysics and cosmology starting from experiment. It provides a unified view of these fields, which is needed to answer our questions to the Universe–a unified view that has been lost somehow in recent years due to increasing specialization. This is the second edition of a book we published only three years ago, a book which had a success beyond our expectations. We felt that the recent progress on gravitational waves, gamma ray and neutrino astrophysics deserved a new edition including all these new developments: multimessenger astronomy is now a reality. In addition, the properties of the Higgs particle are much better known now than three years ago. Thanks to this second edition we had the opportunity to fix some bugs, to extend the material related to exercises, and to change in a more logical form the order of some items. Last but not least, our editor encouraged us a lot to write a second edition. Particle physics has recently seen the incredible success of the so-called standard model. A 50-year long search for the missing ingredient of the model, the Higgs particle, has been concluded successfully, and some scientists claim that we are close to the limit of the physics humans may know. Also astrophysics and cosmology have shown an impressive evolution, driven by experiments and complemented by theories and models. We have nowadays a “standard model of cosmology” which successfully describes the evolution of the Universe from a tiny time after its birth to any foreseeable future. The experimental field of astroparticle physics is rapidly evolving, and its discovery potential appears still enormous: during the three years between the first and the second edition of this book gravitational waves have been detected, an event in which gravitational waves were associated to electromagnetic waves has been detected, and an extragalactic source of astrophysical neutrinos has been located and associated to a gamma-ray emitter. The situation is similar to the one that physics lived at the end of the nineteenth century, after the formulation of Maxwell’s equations—and we know how the story went. As then, there are today some clouds which might hide a new revolution in physics. The main cloud is that experiments indicate that we are still missing the vii
- 13. description of the main ingredients of the Universe from the point of view of its energy budget. We believe one of these ingredients to be a new particle, of which we know very little, and the other to be a new form of energy. The same experi- ments indicating the need for these new ingredients are probably not powerful enough to unveil them, and we must invent new experiments to do it. The scientists who solve this puzzle will base their project on a unified vision of physics, and this book helps to provide such a vision. This book is addressed primarily to advanced undergraduate or beginning graduate students, since the reader is only assumed to know quantum physics and “classical” physics, in particular electromagnetism and analytical mechanics, at an introductory level, but it can also be useful for graduates and postgraduates, and postdoc researchers involved in high-energy physics or astrophysics research. It is also aimed at senior particle and astroparticle physicists as a consultation book. Exercises at the end of each chapter help the reader to review material from the chapter itself and synthesize concepts from several chapters. A “further reading” list is also provided for readers who want to explore in more detail particular topics. Our experience is based on research both at artificial particle accelerators (in our younger years) and in astroparticle physics after the late 1990s. We have worked as professors since more than twenty years, teaching courses on particle and/or astroparticle physics at undergraduate and graduate levels. We spent a long time in several research institutions outside our countries, also teaching there and gaining experience with students with different backgrounds. This book contains a broad and interdisciplinary material, which is appropriate for a consultation book, but it can be too much for a textbook. In order to give coherence to the material for a course, one can think of at least three paths through the manuscript: • For an “old-style” one-semester course on particle physics for students with a good mathematical background, one could select chapters 1, 2, 3, 4, 5, 6, part of 7, and possibly (part of) 8 and 9. • For a basic particle physics course centered in astroparticle physics one could instead use chapters 1, 2, 3, 4 (excluding 4.4), 5.1, 5.2, part of 5.4, part of 5.5, 5.6, 5.7, possibly 6.1, 8.1, 8.4, 8.5, part of 10, and if possible 11. • A one-semester course in high-energy astroparticle physics for students who already know the foundations of particle physics could be based on chapters 1, 3, 4.3.2, 4.5, 4.6, 8, 10, 11; if needed, an introduction to experimental tech- niques could be given based on 4.1 and 4.2. • A specialized half-semester course in high-energy astroparticle physics could be based on chapters 4.3.2, 4.5, 4.6, 8.1, 8.4, 8.5, 10; an introduction to experi- mental techniques could be given based on 4.1 and 4.2 if needed. Unfortunately we know that several mistakes will affect also this second edition. Readers can find at the Web site http://ipap.uniud.it viii Preface
- 14. a “living” errata corrige, plus some extra material related in particular to the exercises. Please help us to improve the book by making suggestions and correc- tions: we shall answer all criticisms with gratitude. Our work would have not been possible without the help of friends and col- leagues; we acknowledge here (in alphabetical order) Pedro Abreu, Sofia Andringa, Stefano Ansoldi, Pedro Assis, Liliana Apolinario, Luca Baldini, Fernando Barão, Sandro Bettini, Giovanni Busetto, Per Carlson, Nuno Castro, Julian Chela-Flores, Stefano Ciprini, Ruben Conceiçao, Jim Cronin, Davide De Grandis, Barbara De Lotto, Michela De Maria, Ivan De Mitri, Pino di Sciascio, Tristano di Girolamo, Jorge Dias de Deus, Anna Driutti, Catarina Espírito Santo, Fernando Ferroni, Alberto Franceschini, Giorgio Galanti, Gianluca Gemme, Riccardo Giannitrapani, Antonella Incicchitti, Giovanni La Mura, Marco Laveder, Claudia Lazzaro, Andrea Longhin, Francesco Longo, Rubén Lopez, Manuela Mallamaci, José Maneira, Ioana Maris, Mauro Mezzetto, Teresa Montaruli, Luc Pape, Alessandro Pascolini, Gianni Pauletta, Elena Pavan, Massimo Persic, Giampaolo Piotto, Piero Rafanelli, Ignasi Reichardt, Jorge Romao, Marco Roncadelli, Sara Salvador, Pablo Saz Parkinson, Ron Shellard, Franco Simonetto, Radomir Smida, Vincent Tatischeff, Bernardo Tomé, Ezio Torassa, Andrea Turcati, Michael Unger, Robert Wagner, Scott Wakely, Alan Watson, Jeff Wyss, Jean-Pierre Zendri. Most of all, we thank all our students who patiently listened and discussed with us during all the past years. Padua, Italy Alessandro De Angelis Lisbon, Portugal Mário Pimenta April 2018 Preface ix
- 15. Contents 1 Understanding the Universe: Cosmology, Astrophysics, Particles, and Their Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Particle and Astroparticle Physics . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Particles and Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The Particles of Everyday Life . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 The Modern View of Interactions: Quantum Fields and Feynman Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 A Quick Look at the Universe . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.7 Multimessenger Astrophysics. . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 Basics of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1 The Atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 The Rutherford Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3 Inside the Nuclei: b Decay and the Neutrino . . . . . . . . . . . . . . 30 2.4 A Look into the Quantum World: Schrödinger’s Equation . . . . 32 2.4.1 Properties of Schrödinger’s Equation and of its Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.2 Uncertainty and the Scale of Measurements . . . . . . . . . 38 2.5 The Description of Scattering: Cross Section and Interaction Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5.1 Total Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5.2 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . 41 2.5.3 Cross Sections at Colliders . . . . . . . . . . . . . . . . . . . . . 41 2.5.4 Partial Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.5.5 Interaction Length . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.6 Description of Decay: Width and Lifetime . . . . . . . . . . . . . . . . 44 2.7 Fermi Golden Rule and Rutherford Scattering . . . . . . . . . . . . . 46 2.7.1 Transition Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.7.2 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 xi
- 16. 2.7.3 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.7.4 Rutherford Cross Section . . . . . . . . . . . . . . . . . . . . . . 50 2.8 Particle Scattering in Static Fields . . . . . . . . . . . . . . . . . . . . . . 50 2.8.1 Extended Charge Distributions (Nonrelativistic) . . . . . . 50 2.8.2 Finite Range Interactions . . . . . . . . . . . . . . . . . . . . . . 51 2.8.3 Electron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.9 Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.9.1 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . 55 2.9.2 Space–Time Interval . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.9.3 Velocity Four-Vector . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.9.4 Energy and Momentum . . . . . . . . . . . . . . . . . . . . . . . 61 2.9.5 Examples of Relativistic Dynamics . . . . . . . . . . . . . . . 64 2.9.6 Mandelstam Variables . . . . . . . . . . . . . . . . . . . . . . . . 65 2.9.7 Lorentz Invariant Fermi Rule . . . . . . . . . . . . . . . . . . . 67 2.9.8 The Electromagnetic Tensor and the Covariant Formulation of Electromagnetism . . . . . . . . . . . . . . . . 69 2.10 Natural Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3 Cosmic Rays and the Development of Particle Physics . . . . . . . . . . 83 3.1 The Puzzle of Atmospheric Ionization and the Discovery of Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.1.1 Underwater Experiments and Experiments Carried Out at Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.1.2 The Nature of Cosmic Rays . . . . . . . . . . . . . . . . . . . . 90 3.2 Cosmic Rays and the Beginning of Particle Physics . . . . . . . . . 90 3.2.1 Relativistic Quantum Mechanics and Antimatter: From the Schrödinger Equation to the Klein–Gordon and Dirac Equations . . . . . . . . . . . . . . . 91 3.2.2 The Discovery of Antimatter . . . . . . . . . . . . . . . . . . . . 95 3.2.3 Cosmic Rays and the Progress of Particle Physics . . . . 97 3.2.4 The l Lepton and the p Mesons . . . . . . . . . . . . . . . . . 98 3.2.5 Strange Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.2.6 Mountain-Top Laboratories . . . . . . . . . . . . . . . . . . . . . 102 3.3 Particle Hunters Become Farmers . . . . . . . . . . . . . . . . . . . . . . 103 3.4 The Recent Years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4 Particle Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.1 Interaction of Particles with Matter . . . . . . . . . . . . . . . . . . . . . 109 4.1.1 Charged Particle Interactions . . . . . . . . . . . . . . . . . . . . 109 4.1.2 Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1.3 Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1.4 Photon Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.1.5 Nuclear (Hadronic) Interactions . . . . . . . . . . . . . . . . . . 123 4.1.6 Interaction of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . 123 xii Contents
- 17. 4.1.7 Electromagnetic Showers . . . . . . . . . . . . . . . . . . . . . . 124 4.1.8 Hadronic Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.2 Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.2.1 Track Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.2.2 Photosensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.2.3 Cherenkov Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.2.4 Transition Radiation Detectors . . . . . . . . . . . . . . . . . . 142 4.2.5 Calorimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.3 High-Energy Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.3.1 Artificial Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.3.2 Cosmic Rays as Very-High-Energy Beams . . . . . . . . . 149 4.4 Detector Systems and Experiments at Accelerators . . . . . . . . . . 150 4.4.1 Examples of Detectors for Fixed-Target Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.4.2 Examples of Detectors for Colliders . . . . . . . . . . . . . . 154 4.5 Cosmic-Ray Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 4.5.1 Interaction of Cosmic Rays with the Atmosphere: Extensive Air Showers . . . . . . . . . . . . . . . . . . . . . . . . 164 4.5.2 Detectors of Charged Cosmic Rays . . . . . . . . . . . . . . . 167 4.5.3 Detection of Hard Photons . . . . . . . . . . . . . . . . . . . . . 175 4.5.4 Neutrino Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4.6 Detection of Gravitational Waves. . . . . . . . . . . . . . . . . . . . . . . 197 5 Particles and Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 5.1 A Zoo of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 5.2 Symmetries and Conservation Laws: The Noether Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.3 Symmetries and Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 5.3.1 A Quantum Mechanical View of the Noether’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 5.3.2 Some Fundamental Symmetries in Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.3.3 Unitary Groups and Special Unitary Groups . . . . . . . . 217 5.3.4 SU(2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 5.3.5 SU(3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 5.3.6 Discrete Symmetries: Parity, Charge Conjugation, and Time Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 5.3.7 Isospin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 5.3.8 The Eightfold Way . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 5.4 The Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 5.4.1 SU(3)flavor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 5.4.2 Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 5.4.3 Excited States (Nonzero Angular Momenta Between Quarks) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Contents xiii
- 18. 5.4.4 The Charm Quark . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 5.4.5 Beauty and Top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 5.4.6 Exotic Hadrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 5.4.7 Quark Families. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 5.5 Quarks and Partons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 5.5.1 Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 5.5.2 Inelastic Scattering Kinematics . . . . . . . . . . . . . . . . . . 243 5.5.3 Deep Inelastic Scattering. . . . . . . . . . . . . . . . . . . . . . . 245 5.5.4 The Quark–Parton Model . . . . . . . . . . . . . . . . . . . . . . 248 5.5.5 The Number of Quark Colors . . . . . . . . . . . . . . . . . . . 253 5.6 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 5.6.1 The Discovery of the ¿ Lepton . . . . . . . . . . . . . . . . . . 256 5.6.2 Three Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 5.7 The Particle Data Group and the Particle Data Book. . . . . . . . . 258 5.7.1 PDG: Estimates of Physical Quantities . . . . . . . . . . . . 259 5.7.2 Averaging Procedures by the PDG . . . . . . . . . . . . . . . 259 6 Interactions and Field Theories. . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 6.1 The Lagrangian Representation of a Dynamical System . . . . . . 267 6.1.1 The Lagrangian and the Noether Theorem . . . . . . . . . . 268 6.1.2 Lagrangians and Fields; Lagrangian Density . . . . . . . . 269 6.1.3 Lagrangian Density and Mass . . . . . . . . . . . . . . . . . . . 270 6.2 Quantum Electrodynamics (QED) . . . . . . . . . . . . . . . . . . . . . . 270 6.2.1 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 6.2.2 Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.2.3 Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 6.2.4 Dirac Equation Revisited . . . . . . . . . . . . . . . . . . . . . . 278 6.2.5 Klein–Gordon Equation Revisited . . . . . . . . . . . . . . . . 290 6.2.6 The Lagrangian for a Charged Fermion in an Electromagnetic Field: Electromagnetism as a Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 6.2.7 An Introduction to Feynman Diagrams: Electromagnetic Interactions Between Charged Spinless Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 6.2.8 Electron–Muon Elastic Scattering (e l ! e l ) . . . . 300 6.2.9 Feynman Diagram Rules for QED . . . . . . . . . . . . . . . . 304 6.2.10 Muon Pair Production from e eþ Annihilation (e eþ ! l lþ ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 6.2.11 Bhabha Scattering e eþ ! e eþ . . . . . . . . . . . . . . . . 308 6.2.12 Renormalization and Vacuum Polarization . . . . . . . . . . 311 6.3 Weak Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 6.3.1 The Fermi Model of Weak Interactions . . . . . . . . . . . . 315 6.3.2 Parity Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 xiv Contents
- 19. 6.3.3 V-A Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 6.3.4 “Left” and “Right” Chiral Particle States . . . . . . . . . . . 322 6.3.5 Intermediate Vector Bosons . . . . . . . . . . . . . . . . . . . . 325 6.3.6 The Cabibbo Angle and the GIM Mechanism . . . . . . . 333 6.3.7 Extension to Three Quark Families: The CKM Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 6.3.8 C P Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 6.3.9 Matter–Antimatter Asymmetry . . . . . . . . . . . . . . . . . . 351 6.4 Strong Interactions and QCD . . . . . . . . . . . . . . . . . . . . . . . . . . 353 6.4.1 Yang–Mills Theories . . . . . . . . . . . . . . . . . . . . . . . . . 354 6.4.2 The Lagrangian of QCD . . . . . . . . . . . . . . . . . . . . . . . 356 6.4.3 Vertices in QCD; Color Factors . . . . . . . . . . . . . . . . . 357 6.4.4 The Strong Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 359 6.4.5 Asymptotic Freedom and Confinement . . . . . . . . . . . . 361 6.4.6 Hadronization; Final States from Hadronic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 6.4.7 Hadronic Cross Section . . . . . . . . . . . . . . . . . . . . . . . 371 7 The Higgs Mechanism and the Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 7.1 The Higgs Mechanism and the Origin of Mass . . . . . . . . . . . . . 395 7.1.1 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . 396 7.1.2 An Example from Classical Mechanics . . . . . . . . . . . . 396 7.1.3 Application to Field Theory: Massless Fields Acquire Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 7.1.4 From SSB to the Higgs Mechanism: Gauge Symmetries and the Mass of Gauge Bosons . . . . . . . . . 400 7.2 Electroweak Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 7.2.1 The Formalism of the Electroweak Theory . . . . . . . . . 403 7.2.2 The Higgs Mechanism in the Electroweak Theory and the Mass of the Electroweak Bosons . . . . . . . . . . . 408 7.2.3 The Fermion Masses . . . . . . . . . . . . . . . . . . . . . . . . . 411 7.2.4 Interactions Between Fermions and Gauge Bosons . . . . 411 7.2.5 Self-interactions of Gauge Bosons . . . . . . . . . . . . . . . . 414 7.2.6 Feynman Diagram Rules for the Electroweak Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 7.3 The Lagrangian of the Standard Model . . . . . . . . . . . . . . . . . . 415 7.3.1 The Higgs Particle in the Standard Model . . . . . . . . . . 415 7.3.2 Standard Model Parameters . . . . . . . . . . . . . . . . . . . . . 416 7.3.3 Accidental Symmetries . . . . . . . . . . . . . . . . . . . . . . . . 419 7.4 Observables in the Standard Model . . . . . . . . . . . . . . . . . . . . . 419 7.5 Experimental Tests of the Standard Model at Accelerators . . . . 422 7.5.1 Data Versus Experiments: LEP (and the Tevatron) . . . . 423 Contents xv
- 20. 7.5.2 LHC and the Discovery of the Higgs Boson . . . . . . . . 436 7.6 Beyond the Minimal SM of Particle Physics; Unification of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 7.6.1 Grand Unified Theories . . . . . . . . . . . . . . . . . . . . . . . 444 7.6.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 7.6.3 Strings and Extra Dimensions; Superstrings . . . . . . . . . 450 7.6.4 Compositeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 8 The Standard Model of Cosmology and the Dark Universe . . . . . . 455 8.1 Experimental Cosmology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 8.1.1 The Universe Is Expanding . . . . . . . . . . . . . . . . . . . . . 456 8.1.2 Expansion Is Accelerating . . . . . . . . . . . . . . . . . . . . . . 461 8.1.3 Cosmic Microwave Background . . . . . . . . . . . . . . . . . 463 8.1.4 Primordial Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . 472 8.1.5 Astrophysical Evidence for Dark Matter . . . . . . . . . . . 477 8.1.6 Age of the Universe: A First Estimate . . . . . . . . . . . . . 485 8.2 General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 8.2.1 Equivalence Principle . . . . . . . . . . . . . . . . . . . . . . . . . 487 8.2.2 Light and Time in a Gravitational Field . . . . . . . . . . . . 487 8.2.3 Flat and Curved Spaces . . . . . . . . . . . . . . . . . . . . . . . 490 8.2.4 Einstein’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 494 8.2.5 The Friedmann–Lemaitre–Robertson–Walker Model (Friedmann Equations) . . . . . . . . . . . . . . . . . . . . . . . . 496 8.2.6 Critical Density of the Universe; Normalized Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 8.2.7 Age of the Universe from the Friedmann Equations and Evolution Scenarios . . . . . . . . . . . . . . . . . . . . . . . 503 8.2.8 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 8.2.9 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 508 8.3 Past, Present, and Future of the Universe . . . . . . . . . . . . . . . . . 510 8.3.1 Early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 8.3.2 Inflation and Large-Scale Structures . . . . . . . . . . . . . . 515 8.4 The KCDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 8.4.1 Dark Matter Decoupling and the “WIMP Miracle” . . . . 522 8.5 What Is Dark Matter Made of, and How Can It Be Found? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 8.5.1 WISPs: Neutrinos, Axions and ALPs. . . . . . . . . . . . . . 527 8.5.2 WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 8.5.3 Other Nonbaryonic Candidates . . . . . . . . . . . . . . . . . . 540 xvi Contents
- 21. 9 The Properties of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 9.1 Sources and Detectors; Evidence of the Transmutation of the Neutrino Flavor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 9.1.1 Solar Neutrinos, and the Solar Neutrino Problem . . . . . 544 9.1.2 Neutrino Oscillation in a Two-Flavor System . . . . . . . . 549 9.1.3 Long-Baseline Reactor Experiments . . . . . . . . . . . . . . 553 9.1.4 Estimation of ”e ! ”l Oscillation Parameters . . . . . . . 554 9.1.5 Atmospheric Neutrinos and the ”l ! ”¿ Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 9.1.6 Phenomenology of Neutrino Oscillations: Extension to Three Families . . . . . . . . . . . . . . . . . . . . 557 9.1.7 Short-Baseline Reactor Experiments, and the Determination of h13 . . . . . . . . . . . . . . . . . . . . 559 9.1.8 Accelerator Neutrino Beams . . . . . . . . . . . . . . . . . . . . 560 9.1.9 Explicit Appearance Experiment . . . . . . . . . . . . . . . . . 562 9.1.10 A Gift from Nature: Geo-Neutrinos . . . . . . . . . . . . . . . 563 9.2 Neutrino Oscillation Parameters . . . . . . . . . . . . . . . . . . . . . . . . 563 9.3 Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 9.3.1 The Constraints from Cosmological and Astrophysical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 9.3.2 Direct Measurements of the Electron Neutrino Mass: Beta Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 9.3.3 Direct Measurements of the Muon- and Tau-Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 9.3.4 Incorporating Neutrino Masses in the Theory . . . . . . . . 569 9.3.5 Majorana Neutrinos and the Neutrinoless Double Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 9.3.6 Present Mass Limits and Prospects . . . . . . . . . . . . . . . 572 10 Messengers from the High-Energy Universe . . . . . . . . . . . . . . . . . . 575 10.1 How Are High-Energy Cosmic Rays Produced? . . . . . . . . . . . . 580 10.1.1 Acceleration of Charged Cosmic Rays: The Fermi Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 580 10.1.2 Production of High-Energy Gamma Rays and Neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 10.1.3 Top-Down Mechanisms; Possible Origin from Dark Matter Particles . . . . . . . . . . . . . . . . . . . . . . . . . 593 10.2 Possible Acceleration Sites and Sources . . . . . . . . . . . . . . . . . . 594 10.2.1 Stellar Endproducts as Acceleration Sites . . . . . . . . . . . 595 10.2.2 Other Galactic Sources . . . . . . . . . . . . . . . . . . . . . . . . 603 10.2.3 Extragalactic Acceleration Sites: Active Galactic Nuclei and Other Galaxies . . . . . . . . . . . . . . . . . . . . . 603 10.2.4 Extragalactic Acceleration Sites: Gamma Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Contents xvii
- 22. 10.2.5 Gamma Rays and the Origin of Cosmic Rays: The Roles of SNRs and AGN . . . . . . . . . . . . . . . . . . . 610 10.2.6 Sources of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 614 10.2.7 Sources of Gravitational Waves. . . . . . . . . . . . . . . . . . 616 10.3 The Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 10.3.1 Magnetic Fields in the Universe . . . . . . . . . . . . . . . . . 618 10.3.2 Photon Background . . . . . . . . . . . . . . . . . . . . . . . . . . 619 10.3.3 Propagation of Charged Cosmic Rays . . . . . . . . . . . . . 619 10.3.4 Propagation of Photons . . . . . . . . . . . . . . . . . . . . . . . . 626 10.3.5 Propagation of Neutrinos . . . . . . . . . . . . . . . . . . . . . . 630 10.3.6 Propagation of Gravitational Waves. . . . . . . . . . . . . . . 630 10.4 More Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 10.4.1 Charged Cosmic Rays: Composition, Extreme Energies, Correlation with Sources . . . . . . . . . . . . . . . 631 10.4.2 Photons: Different Source Types, Transients, Fundamental Physics . . . . . . . . . . . . . . . . . . . . . . . . . 645 10.4.3 Astrophysical Neutrinos . . . . . . . . . . . . . . . . . . . . . . . 662 10.4.4 Gravitational Radiation . . . . . . . . . . . . . . . . . . . . . . . . 666 10.5 Future Experiments and Open Questions . . . . . . . . . . . . . . . . . 671 10.5.1 Charged Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . 671 10.5.2 Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673 10.5.3 The PeV Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 10.5.4 High Energy Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . 674 10.5.5 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 676 10.5.6 Multi-messenger Astrophysics . . . . . . . . . . . . . . . . . . . 677 11 Astrobiology and the Relation of Fundamental Physics to Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683 11.1 What Is Life? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684 11.1.1 Schrödinger’s Definition of Life . . . . . . . . . . . . . . . . . 685 11.1.2 The Recipe of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 11.1.3 Life in Extreme Environments. . . . . . . . . . . . . . . . . . . 690 11.1.4 The Kickoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691 11.2 Life in the Solar System, Outside Earth . . . . . . . . . . . . . . . . . . 692 11.2.1 Planets of the Solar System. . . . . . . . . . . . . . . . . . . . . 693 11.2.2 Satellites of Giant Planets . . . . . . . . . . . . . . . . . . . . . . 695 11.3 Life Outside the Solar System, and the Search for Alien Civilizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 11.3.1 The “Drake Equation” . . . . . . . . . . . . . . . . . . . . . . . . 697 11.3.2 The Search for Extrasolar Habitable Planets . . . . . . . . . 699 11.3.3 The Fermi Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 xviii Contents
- 23. 11.3.4 Searching for Biosignatures. . . . . . . . . . . . . . . . . . . . . 702 11.3.5 Looking for Technological Civilizations: Listening to Messages from Space . . . . . . . . . . . . . . . . . . . . . . . 703 11.3.6 Sending Messages to the Universe . . . . . . . . . . . . . . . 706 11.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Appendix A: Periodic Table of the Elements . . . . . . . . . . . . . . . . . . . . . . 711 Appendix B: Properties of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Appendix C: Physical and Astrophysical Constants . . . . . . . . . . . . . . . . . 715 Appendix D: Particle Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Contents xix
- 24. About the Authors Alessandro De Angelis is a high-energy physicist and astrophysicist. Professor at the Universities of Udine, Padua and Lisbon, he is currently the Principal Investigator of the proposed space mission e-ASTROGAM, and for many years has been director of research at INFN Padua, and scientific coordinator and chairman of the board managing the MAGIC gamma-ray telescopes in the Canary Island of La Palma. His main research interest is on fundamental physics, especially astrophysics and ele- mentary particle physics at accelerators. He graduated from Padua, was employed at CERN for seven years in the 1990s ending as a staff member, and later was among the founding members of NASA’s Fermi gamma-ray telescope. His original scientific contributions have been mostly related to electromagnetic calorimeters, advanced trigger systems, QCD, artificial neural networks, and to the study of the cosmological propagation of photons. He has taught electromagnetism and astroparticle physics in Italy and Portugal and has been a visiting professor in the ICRR of Tokyo, at the Max-Planck Institute in Munich, and at the University of Paris VI. Mário Pimenta is a high-energy physicist and astrophysicist. Professor at the Instituto Superior Técnico of the University of Lisbon, he is currently the president of the Portuguese national organization for Particle and Astroparticle Physics, coordinator of the international Ph.D. doctoral network IDPASC, and the repre- sentative for Portugal at the Pierre Auger Observatory in Argentina. Formerly member of the WA72, WA74, NA38 and DELPHI experiments at CERN and of the EUSO collaboration at ESA, his main interest of research is on high-energy phy- sics, especially cosmic rays of extremely high energy and development of detectors for astroparticle physics. He graduated from Lisbon and Paris VI, and was employed at CERN in the late 1980s. His original contributions have been mostly related to advanced trigger systems, search for new particles, hadronic interactions at extremely high energies, and recently to innovative particle detectors. He has taught general physics and particle physics in Portugal, has lectured at the University of Udine and has been visiting professor at SISSA/ISAS in Trieste. xxi
- 25. Acronyms a.s.l. Above sea level (altitude) ACE Advanced composition explorer (astrophysical observatory orbiting the Earth) AGASA Akeno giant air shower array (experiment in Japan) AGILE Astro-rivelatore gamma a immagini leggero (gamma-ray tele- scope orbiting the Earth) AGN Active galactic nucleus ALEPH A LEP experiment (at CERN) ALICE A large ion collider experiment (at CERN) ALLEGRO A Louisiana low-temperature experimental gravitational radiation observatory (in the USA) ALP Axion-like particle ALPHA Antihydrogen experiment at CERN AMS Alpha magnetic spectrometer (particle detector onboard the ISS) ANTARES Astronomy with a neutrino telescope and abyss environmental research (experiment in the Mediterranean Sea) APD Avalanche photodiode (detector) ARGO-YBJ Cosmic-ray detector at the Yanbanjing Observatory (in Tibet) ATIC Advanced thin ionization calorimeter (balloon-borne experiment) ATLAS A toroidal LHC apparatus (experiment at CERN) AU Astronomical unit (a.u.) AURIGA An ultracryogenic gravitational waves detector BaBar B–anti-B experiment at SLAC BATSE Burst and transient source experiment (in the CGRO) BBN Big Bang nucleosynthesis BEBC Big European Bubble Chamber (experiment at CERN) Belle b physics experiment at KEK BESS Balloon-borne experiment with superconducting spectrometer Bevatron Billion electron volts synchrotron (accelerator in the USA) BGO Bi4 Ge3 O12 (scintillating crystal) xxiii
- 26. BH Black hole BL Lac Blazar Lacertae (an active galactic nucleus) BNL Brookhaven National Laboratory (in Long Island, NY) Borexino Boron solar neutrino experiment (at the LNGS) BR Branching ratio (in a decay process) CANGAROO Collaboration of Australia and Nippon (Japan) for a gamma-ray observatory in the outback (Cherenkov observatory) CAST CERN axion search telescope (experiment at CERN) CDF Collider detector at Fermilab (experiment) KCDM Lambda and cold dark matter (model with cosmological constant K) CERN European Organization for Nuclear Research, also European laboratory for particle physics CGC Colour glass condensate CGRO Compton gamma-ray observatory (orbiting the Earth) cgs centimeter, gram, second (system of units) CKM Cabibbo, Kobayasha, Maskawa (matrix mixing the quark flavors.) CMB Cosmic microwave background (radiation) CMS Compact Muon Solenoid (experiment at CERN) COBE Cosmic Background Explorer (satellite orbiting the Earth) CoGeNT Coherent germanium neutrino telescope (experiment in the USA) COUPP Chicagoland observatory for underground particle physics (experiment at Fermilab) CP Charge conjugation Parity (product of symmetry operators) CPT Charge conjugation Parity Time reversal (product of symmetry operators) CR Cosmic rays CREAM Cosmic-ray energetics and mass experiment (now on the ISS) CRESST Cryogenic rare event search with superconducting thermometers (experiment at LNGS) CTA Cherenkov Telescope Array (an international gamma-ray detector) CUORE Cryogenic underground observatory for rare events (experiment at LNGS) D0 Experiment at Fermilab DAMA Dark matter experiment (at LNGS) DAMPE Dark matter particle explorer (astrophysical space observatory) DAQ Data acquisition (electronics system) DARMa De Angelis, Roncadelli, Mansutti (model of axion-photon mixing) DAS Data acquisition system DASI Degree angular scale interferometer DELPHI Detector with lepton, photon, and hadron identification (experiment at the CERN’s LEP) xxiv Acronyms
- 27. DESY Deutsche synchrotron (laboratory in Germany) DM Dark matter DNA Desoxyribonucleic acid (the genetic base of life) DONUT Direct observation of the ”¿ (experiment at Fermilab) DSA Diffusive shock acceleration (of cosmic rays) dSph Dwarf spheroidal galaxy EAS Extensive air shower (cosmic rays) EBL Extragalactic background light ECAL Electromagnetic calorimeter (detector) EGMF Extragalactic magnetic field EGO European Gravitational Observatory (in Italy) EGRET Energetic gamma-ray experiment telescope (part of the CGRO) EHE Extremely high energy EHS European hybrid spectrometer (experiment at CERN) EJSM/Laplace European Jupiter space mission–Laplace (ESA/NASA Mission) ESA European Space Agency EUSO Extreme Universe Space Observatory FCNC Flavor-changing neutral currents (hypothetical electroweak process) FD Fluorescence detector Fermilab Fermi National Accelerator Laboratory (near Chicago, IL); also FNAL FLRW Friedmann, Lemaitre, Robertson, Walker (metric model in general relativity) FNAL Fermi National Accelerator Laboratory (near Chicago, IL); also Fermilab FoV Field of view FPGA Field-programmable gate array (processor) FRI Fanaroff and Riley class I (astrophysical sources) FSRQ Flat spectrum radio quasars GALLEX Gallium experiment (at LNGS) GAMMA-400 gamma-ray space observatory (space astrophysical observatory) Gargamelle Experiment at CERN GBM Gamma Burst Monitor (detector) GC Galactic center GERDA Germanium detector array (experiment at the LNGS) GIM Glashow, Iliopoulos, Maiani (mechanism) GLAST Gamma-ray large area space telescope, renamed Fermi after positioning in orbit GPM Gaseous photomultipliers GPS Global positioning system GRB Gamma-ray burst (astrophysical event) GSW Glashow–Salam–Weinberg model of electroweak unification GUT Grand unified theory GZK Greisen, Zatsepin, Kuz’min (energy cutoff for cosmic rays) Acronyms xxv
- 28. H.E.S.S. High-energy stereoscopic system (Cherenkov experiment in Namibia) HAWC High-altitude water Cherenkov (observatory in Mexico) HBL High-energy peaked BL Lac HCAL Hadron calorimeter (detector) HE High energy HEGRA High-energy gamma-ray astronomy (Cherenkov experiment in La Palma) HERA Hadron elektron ring anlage (particle accelerator at DESY) HPD Hybrid photon detector HST Hubble Space Telescope (orbiting the Earth) IACT Imaging Atmospheric Cherenkov Telescope IBL Intermediate energy peaked BL Lac IC Inverse Compton scattering (mechanism for the production of HE gamma rays) IceCube Neutrinos observatory in Antarctica ICRR Institute for Cosmic Ray Research (at the University of Tokyo, Japan) IDPASC International doctorate on particle and astroparticle physics, astrophysics, and cosmology (doctoral network) IMB Irvine, Michigan, Brookhaven (experiment in the US) INFN Istituto Nazionale di Fisica Nucleare (in Italy) IR Infrared (radiation) IRB Infrared background (photons) ISS International Space Station IST Instituto Superior Técnico (at the University of Lisboa, Portugal) JEM Japanese experimental module (onboard the ISS) K2K KEK to Kamioka experiment (Japan) Kamiokande Kamioka neutrino detector (experiment in Japan) KamLAND Kamioka liquid scintillator antineutrino detector (experiment in Japan) KASCADE Karlsruhe shower and cosmic array detector (experiment in Germany) KATRIN Karlsruhe tritium neutrino experiment (in Germany) KEK High-energy accelerator in Japan Kepler Mission to search for extraterrestrial planets (NASA) KM Parametrization of the CKM matrix in the original paper by Kobayasha and Maskawa Km3NeT kilometer cube neutrino telescope (experiment in the Mediterranean Sea) kTeV Experiment at Fermilab L3 LEP third (experiment at CERN) LAr Liquid argon LAT Large Area Telescope (detector on the Fermi Satellite) Fermi-LAT Large Area Tracker, a gamma-ray telescope orbiting the Earth xxvi Acronyms
- 29. LBL Low-energy peaked BL Lac LEBC LExan Bubble Chamber (experiment at CERN) LEP II Second phase of operation of LEP, at energies above the Z mass LEP Large electron positron (collider at CERN) LHC Large hadron collider (at CERN) LHCb LHC beauty (experiment at CERN) LHCf LHC forward (experiment at CERN) LIGO Laser interferometer gravitational-wave observatory (in the USA) LISA Laser interferometer space antenna (project for gravitational wave’s detection) LIV Lorentz invariance violation LMC Large Magellanic Cloud (dwarf galaxy satellite of the Milky Way) LNGS Laboratorio Nazionale del Gran Sasso (Laboratory for particle and astroparticle physics in Italy) LO Leading order in perturbative expansions LPHD Local parton hadron duality (approximation in QCD predictions) LPM Landau–Pomeranchuk–Migdal (effect) LSND Liquid scintillator neutrino detector (experiment in the USA) LSP Lightest supersymmetric particle LST Large-size telescope (Cherenkov telescope for CTA) ly light-year MACE Major atmospheric cherenkov experiment (Cherenkov experi- ment in India) MACHO Massive astronomical compact halo object MAGIC Major atmospheric gamma-ray imaging Cherenkov telescopes (Cherenkov experiment in Canary Islands) MARE Microcalorimeter arrays for a Rhenium experiment (in Italy) MC Monte Carlo (simulation technique) MILAGRO Cosmic-ray (gamma in particular) experiment in the USA MINOS Main injector neutrino oscillation search (experiment in Fermilab) mip minimum ionizing particle MoEDAL Monopole and exotics detector at the LHC (experiment at CERN) MOND Modified Newtonian dynamics MSSM Minimal supersymmetric model MSW Mikheyev, Smirnov, Wolfenstein (matter effect in neutrino oscillations) NA# North area # (experiment at CERN, # standing for its number) NASA National Aeronautics and Space Agency (in the USA) NEMO Neutrino Ettore Majorana Observatory (in France) NESTOR Neutrino Extended Submarine Telescope with Oceanographic Research (experiment in the Mediterranean Sea) NFW Navarro, Frenk and White (profile of dark matter distribution) NIST National Institute of Standards and Technology (US institute) Acronyms xxvii
- 30. NKG Nishimura Kamata Greisen (lateral density distribution function for showers) NLO Next-to-leading order in QCD perturbative expansions NLSP Next-to-lightest supersymmetric particle NNLO Next-to-next-to-leading order in perturbative expansions NS Neutron star NT-200 Neutrino telescope (experiment in Russia) NTP Normal temperature and pressure NU Natural units (system of units) OPAL Omni-purpose apparatus for LEP (experiment at CERN) OPERA Oscillation project with emulsion-tracking apparatus (experiment at LNGS) OZI Okubo Zweig Iizuka (rule for transitions in particle processes) PAMELA Payload for antimatter–matter exploration and light-nuclei astro- physics (astrophysical observatory orbiting the Earth) PAO Pierre Auger Observatory (cosmic-ray observatory in Argentina) PDF Parton density function PDG Particle Data Group PHENIX A physics experiment at RHIC Planck ESA mission for precise measurement of CMB anisotropy and other properties PLATO Planet transits and oscillations of stars (ESA mission to search for extraterrestrial planets) PMNS Pontecorvo, Maki, Nakagawa, Sakata (neutrino mixing matrix) PMT Photomultiplier tube (detector) PSF Point spread function (space or angular resolution) PVLAS Polarizzazione del vuoto con laser (experiment in Italy) PWN Pulsar wind nebula (astrophysical object) QCD Quantum chromodynamics QED Quantum electrodynamics QG Quantum gravity QGP Quark gluon plasma (state of matter) QPM Quark parton model RF Radiofrequency RHIC Relativistic Heavy Ion Collider (at BNL) RICH Ring imaging Cherenkov (detector) RMS Root mean square RPC Resistive plate chamber (detector) SAGE Soviet–American gallium experiment (in Russia) SCT Semiconductor tracker (detector) SDP Shower detector plane (cosmic rays) SED Spectral energy distribution SETI Seach for extraterrestrial intelligence SI International system (of units) SiPM Silicon photomultiplier (detector) xxviii Acronyms
- 31. SK Super-Kamiokande neutrino detector (experiment in Japan); also Super-K SLAC Stanford linear accelerator center (in the USA) SLD SLAC large detector SM Standard model (of particle physics) SMBH Supermassive black hole SMC Small Magellanic Cloud (dwarf galaxy satellite of the Milky Way) SNO Sudbury neutrino observatory (Canada) SNR Supernova remnant SNU Solar neutrino unit (of neutrino interactions) SO(n) Special orthogonal group of rank n SPEAR Stanford Positron Electron Asymmetric Rings (particle acceler- ator in the USA) SPS Super-proton synchrotron (particle accelerator at CERN) Sp pS Super-proton–antiproton synchrotron (collider at CERN) SSB Spontaneous symmetry breaking SSC Self-synchrotron Compton (mechanism for production of HE gamma-rays) SSM Standard solar model (of physics reactions in the Sun’s core) SU(n) Special unitary group of rank n Super-K Super-Kamiokande neutrino detector (experiment in Japan); also SK SUSY Supersymmetry (model beyond the SM) T2K Tokai to Kamioka experiment (in Japan) TA Telescope Array (cosmic-ray observatory in the USA) TDAQ Trigger and data acquisition (electronics system) Tevatron Teraelectronvolt synchrotron (collider at Fermilab) TeVCAT Catalog of astrophysical VHE gamma-ray sources TGC Triple gauge coupling (coupling between the electroweak gauge bosons—Z; W bosons, and the photon) Tibet-AS Cosmic-ray experiment TMAE Tetra dimethyl-amine ethylene TNT Trinitrotoluene (2-Methyl-1,3,5-trinitrobenzene, chemical explosive) TOTEM Total cross section, elastic scattering and diffraction dissociation at the LHC (experiment at CERN) TPC Time projection chamber (detector) TRD Transition radiation detector TRT Transition radiation tracker (detector) U(n) Unitary group of rank n UA# Underground area # (experiment at CERN, # standing for its number) UHE Ultrahigh-energy (cosmic rays) UHECR Ultrahigh-energy cosmic rays Acronyms xxix
- 32. UV Ultraviolet (radiation) V–A Vector minus axial-vector relational aspect of a theory VCV Véron-Cetty Véron (catalog of galaxies with active galactic nuclei) VERITAS Very energetic radiation imaging telescope array system (Cherenkov experiment in the USA) VHE Very high-energy (cosmic rays) VIRGO Italian-French laser interferometer collaboration at EGO (exper- iment in Italy) VLBA Very long baseline array (of radio telescopes, in the USA) WA# West area # (experiment at CERN, # standing for its number) WBF Weak boson fusion (electroweak process) WHIPPLE Cherenkov telescope (in Arizona) WIMP Weakly interactive massive particle WMAP Wilkinson microwave anisotropy probe (satellite orbiting the Earth) XCOM Photon cross sections database by NIST XTR X-ray transition radiation xxx Acronyms
- 33. Chapter 1 Understanding the Universe: Cosmology, Astrophysics, Particles, and Their Interactions Cosmology, astrophysics, and the physics of elementary particles and interactions are intimately connected. After reading this chapter, it will be clear that these subjects are part of the same field of investigation: this book will show you some of the connections, and maybe many more you will discover yourself in the future. 1.1 Particle and Astroparticle Physics The Universe around us, the objects surrounding us, display an enormous diversity. Is this diversity built over small hidden structures? This interrogation started out, as it often happens, as a philosophical question, only to become, several thousand years later, a scientific one. In the sixth and fifth century BC in India and Greece the atomic concept was proposed: matter was formed by small, invisible, indivisible, and eternal particles: the atoms—a word invented by Leucippus (460 BC) and made popular by his disciple Democritus. In the late eighteenth and early nineteenth century, chemistry gave finally to atomism the status of a scientific theory (mass conservation law, Lavoisier 1789; ideal gas laws, Gay-Lussac 1802; multiple proportional law, Dalton 1805), which was strongly reinforced with the establishment of the periodic table of elements by Mendeleev in 1869—the chemical properties of an element depend on a “magic” number, its atomic number. If atoms did exist, their shape and structure were to be discovered. For Dalton, who lived before the formalization of electromagnetism, atoms had to be able to establish mechanical links with each other. After Maxwell (who formulated the electromag- netic field equations) and J.J. Thomson (who discovered the electron) the binding force was supposed to be the electric one and in atoms an equal number of positive and © Springer International Publishing AG, part of Springer Nature 2018 A. De Angelis and M. Pimenta, Introduction to Particle and Astroparticle Physics, Undergraduate Lecture Notes in Physics, https://doi.org/10.1007/978-3-319-78181-5_1 1
- 34. 2 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.1 Sketch of the atom according to atomic models by several scientists in the early twentieth century: from left to right, the Lenard model, the Nagaoka model, the Thomson model, and the Bohr model with the constraints from the Rutherford experiment. Source: http://skullsinthestars. com/2008/05/27/the-gallery-of-failed-atomic-models-1903-1913 negative electric charges had to be accommodated in stable configurations. Several solutions were proposed (Fig.1.1), from the association of small electric dipoles by Philip Lenard (1903) to the Saturnian model of Hantora Nagaoka (1904), where the positive charges were surrounded by the negative ones like the planet Saturn and its rings. In the Anglo-Saxon world the most popular model was, however, the so-called plum pudding model of Thomson (1904), where the negative charges, the electrons, were immersed in a “soup” of positive charges. This model was clearly dismissed by Rutherford, who demonstrated in the beginning of the twentieth century that the positive charges had to be concentrated in a very small nucleus. Natural radioactivity was the first way to investigate the intimate structure of matter; then people needed higher energy particles to access smaller distance scales. These particles came again from natural sources: it was discovered in the beginning of the twentieth century that the Earth is bombarded by very high-energy particles coming from extraterrestrial sources. These particles were named “cosmic rays.” A rich and not predicted spectrum of new particles was discovered. Particle physics, the study of the elementary structure of matter, also called “high-energy physics,” was born. High-energy physics is somehow synonymous with fundamental physics. The reason is that, due to Heisenberg’s1 principle, the minimum scale of distance ∆x we can sample is inversely proportional to the momentum (which approximately equals the ratio of the energy E by the speed of light c for large energies) of the probe we are using for the investigation itself: ∆x ≃ ∆p ≃ p . 1Werner Heisenberg (1901–1976) was a German theoretical physicist and was awarded the 1932 Nobel Prize in Physics “for the creation of quantum mechanics.” He also contributed to the theories of hydrodynamics, ferromagnetism, cosmic rays, and subatomic physics. During World War II he worked on atomic research, and after the end of the war he was arrested, then rehabilitated. Finally he organized the Max Planck Institute for Physics, which is named after him.
- 35. 1.1 Particle and Astroparticle Physics 3 In the above equation, = h/2π ≃ 10−34 J s is the so-called Planck2 constant (some- times the name of Planck constant is given to h). Accelerating machines, developed in the mid-twentieth century, provided higher and higher energy particle beams in optimal experimental conditions. The collision point was well-defined and multilayer detectors could be built around it. Subnuclear particles (quarks) were discovered, and a “standard model of particle physics” was built, piece by piece, until its final con- secration with the recent discovery of the Higgs boson. The TeV energy scale (that corresponds to distances down to 10−19 –10−20 m) is, for the time being, understood. However, at the end of the twentieth century, the “end of fundamental physics research” announced once again by some, was dramatically dismissed by new and striking experimental evidence which led to the discovery of neutrino oscillations, which meant nonzero neutrino mass, and by the proof that the Universe is in a state of accelerated expansion and that we are immersed in a dark Universe composed mainly of dark matter and dark energy—whatever those entities, presently unknown to us, are. While the discovery that neutrinos have nonzero mass could be incorporated in the standard model by a simple extension, the problems of dark matter and dark energy are still wide open. The way to our final understanding of the fundamental constituents of the Uni- verse, which we think will occur at energies of 1019 GeV (the so-called Planck scale), is hopelessly long. What is worse, despite the enormous progress made by particle acceleration technology, the energies we shall be able to reach at Earth will always be lower than those of the most energetic cosmic rays—particles reaching the Earth from not yet understood extraterrestrial accelerators. These high-energy beams from space may advance our knowledge of fundamental physics and interactions, and of astrophysical phenomena; last but not least, the messengers from space may advance our knowledge of the Universe on a large scale, from cosmology to the ultimate quest on the origins of life, astrobiology. That is the domain and the ambition of the new field of fundamental physics called astroparticle physics. This book addresses this field. Let us start from the fundamental entities: particles and their interactions. 1.2 Particles and Fields The paradigm which is currently accepted by most researchers, and which is at the basis of the so-called standard model of particle physics, is that there is a set of elementary particles constituting matter. From a philosophical point of view, even the very issue of the existence of elementary particles is far from being established: 2Max Planck (1858–1934) was the originator of quantum theory, and deeply influenced the human understanding of atomic and subatomic processes. Professor in Berlin, he was awarded the Nobel Prize in 1918 “in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.” Politically aligned with the German nationalistic positions during World War I, Planck was later opposed to Nazism. Planck’s son, Erwin, was arrested after an assassination attempt of Hitler and died at the hands of the Gestapo.
- 36. 4 1 Understanding the Universe: Cosmology, Astrophysics, Particles… the concept of elementarity may just depend on the energy scale at which matter is investigated—i.e., ultimately, on the experiment itself. And since we use finite energies, a limit exists to the scale one can probe. The mathematical description of particles, in the modern quantum mechanical view, is that of fields, i.e., of complex amplitudes associated to points in spacetime, to which a local probability can be associated. Interactions between elementary particles are described by fields representing the forces; in the quantum theory of fields, these fields can be seen as particles them- selves. In classical mechanics fields were just a mathematical abstraction; the real thing were the forces. The paradigmatic example was Newton’s3 instantaneous and universal gravitation law. Later, Maxwell gave to the electromagnetic field the status of a physical entity: it transports energy and momentum in the form of electromag- netic waves and propagates at a finite velocity—the speed of light. Then, Einstein4 explained the photoelectric effect postulating the existence of photons—the interac- tion of the electromagnetic waves with free electrons, as discovered by Compton,5 was equivalent to elastic collisions between two particles: the photon and the elec- tron. Finally with quantum mechanics the wave-particle duality was extended to all “field” and “matter” particles. Field particles and matter particles have different behaviors. Whereas matter par- ticles comply with the Pauli6 exclusion principle—only one particle can occupy a given quantum state (matter particles obey Fermi-Dirac statistics and are called 3Sir Isaac Newton (1642–1727) was an English physicist, mathematician, astronomer, alchemist, and theologian, who deeply influenced science and culture down to the present days. His mono- graph Philosophiae Naturalis Principia Mathematica (1687) provided the foundations for classical mechanics. Newton built the first reflecting telescope and developed theories of color and sound. In mathematics, Newton developed differential and integral calculus (independently from Leibnitz). Newton was also deeply involved in occult studies and interpretations of religion. 4Albert Einstein (1879–1955) was a German-born physicist who deeply changed the human rep- resentation of the Universe, and our concepts of space and time. Although he is best known by the general public for his theories of relativity and for his mass-energy equivalence formula E = mc2 (the main articles on the special theory of relativity and the E = mc2 articles were published in 1905), he received the 1921 Nobel Prize in Physics “especially for his discovery of the law of the photoelectric effect” (also published in 1905), which was fundamental for establishing quan- tum theory. The young Einstein noticed that Newtonian mechanics could not reconcile the laws of dynamics with the laws of electromagnetism; this led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to accelerated frames of reference when one was including gravitational fields, which led to his general theory of relativity (1916). A professor in Berlin, he moved to the USA when Adolf Hitler came to power in 1933, becoming a US citizen in 1940. During World War II, he cooperated with the Manhattan Project, which led to the atomic bomb. Later, however, he took a position against nuclear weapons. In the USA, Einstein was affiliated with the Institute for Advanced Study in Princeton. 5Arthur H. Compton (1892–1962) was awarded the Nobel Prize in Physics in 1927 for his 1923 discovery of the now-called Compton effect, which demonstrated the particle nature of electromag- netic radiation. During World War II, he was a key figure in the Manhattan Project. He championed the idea of human freedom based on quantum indeterminacy, 6Wolfgang Ernst (the famous physicist Ernst Mach was his godfather) Pauli (Vienna, Austria, 1900—Zurich,Switzerland,1958)wasawardedthe1945Nobelprizeinphysics“forthediscoveryof the exclusion principle, also called the Pauli principle.” He also predicted the existence of neutrinos. Professor in ETH Zurich and in Princeton, he had a rich exchange of letters with psychologist Carl
- 37. 1.2 Particles and Fields 5 “fermions”)—there is no limit to the number of identical and indistinguishable field particles that can occupy the same quantum state (field particles obey Bose–Einstein statistics and are called “bosons”). Lasers (coherent streams of photons) and the electronic structure of atoms are thus justified. The spin of a particle and the statis- tics it obeys are connected by the spin-statistics theorem: according to this highly nontrivial theorem, demonstrated by Fierz (1939) and Pauli (1940), fermions have half-integer spins, whereas bosons have integer spins. At the present energy scales and to our current knowledge, there are 12 elementary “matter” particles; they all have spin 1/2, and hence, they are fermions. The 12 “matter particles” currently known can be divided into two big families: 6 leptons (e.g., the electron, of charge −e, and the neutrino, neutral), and 6 quarks (a state of 3 bound quarks constitutes a nucleon, like the proton or the neutron). Each big family can be divided into three generations of two particles each; generations have similar properties—but different masses. This is summarized in Fig.1.2. A good scale for masses is one GeV/c2 , approximately equal to 1.79 ×10−27 kg— we are implicitly using the relation E = mc2 ; the proton mass is about 0.938 GeV/c2 . Notice, however, that masses of the elementary “matter” particles vary by many orders of magnitude, from the neutrino masses which are of the order of a fraction of eV/c2 , to the electron mass (about half a MeV/c2 ), to the top quark mass (about 173 GeV/c2 ). Quarks have fractional charges with respect to the absolute value of the electron charge, e: 2 3 e for the up, charm, top quark, and −1 3 e for the down, strange, bottom. Quark names are just fantasy names. The material constituting Earth can be basically explained by only three particles: the electron, the up quark, and the down quark (the proton being made of two up quarks and one down, uud, and the neutron by one up and two down, udd). For each known particle there is an antiparticle (antimatter) counterpart, with the same mass and opposite charge quantum numbers. To indicate antiparticles, the following convention holds: if a particle is indicated by P, its antiparticle is in general written with a bar over it, i.e., P̄. For example, to every quark, q, an antiquark, q̄, is associated; the antiparticle of the proton p (uud) is the antiproton p̄ (ūūd̄), with negative electric charge. The antineutron n̄ is the antiparticle of the neutron (note the different quark composition of the two). To the electron neutrino νe an anti-electron neutrino ν̄e corresponds (we shall see later in the book that neutrinos, although electrically neutral, have quantum numbers allowing them to be distinguished from their antiparticles). A different naming convention is used in the case of the anti- electron or positron e+ : the superscript denoting the charge makes explicit the fact that the antiparticle has the opposite electric charge to that of its associated particle. The same applies to the heavier leptons (μ± , τ± ) and to the “field particles” W± . At thecurrent energyscales of theUniverse, particles interact viafour fundamental interactions. There are indications that this view is related to the present-day energy of the Universe: at higher energies—i.e., earlier epochs—some interactions would “unify” and the picture would become simpler. In fact, theorists think that these Gustav Jung. According to anecdotes, Pauli was a very bad experimentalist, and the ability to break experimental equipment simply by being in the vicinity was called the “Pauli effect.”
- 38. 6 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.2 Presently observed elementary particles. Fermions (the matter particles) are listed in the first three columns; gauge bosons (the field particles) are listed in the fourth column. The Higgs boson is standing alone. Adapted from MissMJ [CC BY 3.0 (http://creativecommons.org/licenses/ by/3.0)], via Wikimedia Commons interactions might be the remnants of one single interaction that would occur at extreme energies—e.g., the energies typical of the beginning of the Universe. By increasing order of strength: 1. The gravitational interaction, acting between whatever pair of bodies and domi- nant at macroscopic scales. 2. The electromagnetic interaction, acting between pairs of electrically charged par- ticles (i.e., all matter particles, excluding neutrinos). 3. The weak interaction, also affecting all matter particles (with certain selection rules) and responsible, for instance, for the beta decay and thus for the energy production in the Sun. 4. The color force, acting among quarks. The strong interaction,7 responsible for binding the atomic nuclei (it ensures electromagnetic repulsion among protons 7This kind of interaction was first conjectured and named by Isaac Newton at the end of the seventeenth century: “There are therefore agents in nature able to make the particles of bodies stick together by very strong attractions. And it is the business of experimental philosophy to find them out. Now the smallest particles of matter may cohere by the strongest attractions and compose bigger particles of weaker virtue; and many of these may cohere and compose bigger particles whose virtue is still weaker, and so on for diverse successions, until the progression ends in the biggest particles on which the operations in chemistry, and the colors of natural bodies depend.” (I. Newton, Opticks).
- 39. 1.2 Particles and Fields 7 in nuclei does not break them up) and for the interaction of cosmic protons with the atmosphere, is just a residual shadow (à la van der Waals) of the very strong interaction between quarks. The relative intensity of such interactions spans many orders of magnitude. In a 2 H atom, in a scale where the intensity of strong interactions between the nucleons is 1, the intensity of electromagnetic interactions between electrons and the nucleus is 10−5 , the intensity of weak interactions is 10−13 , and the intensity of gravitational interactions between the electron and the nucleus is 10−45 . However, intensity is not the only relevant characteristic in this context: one should consider also the range of the interactions and the characteristics of the charges. The weak and strong interac- tions act at subatomic distances, smaller than ∼1 fm, and they are not very important at astronomical scales. The electromagnetic and gravitational forces have instead a 1/r2 dependence. On small (molecular) scales, gravity is negligible compared to electromagnetic forces; but on large scales, the universe is electrically neutral, so that electrostatic forces become negligible. Gravity, the weakest of all forces from a particle physics point of view, is the force determining the evolution of the Universe at large scales. In the quantum mechanical view of interactions, the interaction itself is mediated by quanta of the force field. Quanta of the interaction fields Strong interaction Eight gluons Electromagnetic interaction Photon (γ) Weak interaction Bosons W+, W−, Z Gravitational interaction Graviton (?) According to most scientists, the gravitational interaction is mediated by the graviton, an electrically neutral boson of mass 0 and spin 2, yet undiscovered. The weak interaction is mediated by three vectors: two are charged, the W+ (of mass ∼80.4GeV/c2 ) and its antiparticle, the W− ; one is neutral, the Z (with mass ∼91.2GeV/c2 ). The electromagnetic interaction is mediated by the well-known pho- ton. The color interaction is exchanged by eight massless neutral particles called glu- ons. The couplings of each particle to the boson(s) associated to a given interaction are determined by the strength of the interaction and by “magic” numbers, called charges. The gravitational charge of a particle is proportional to its mass (energy); the weak charge is the weak isospin charge (±1/2 for the fermions sensitive to the weak interaction, 0, ±1 for bosons); the electrical charge is the well-known (positive and negative) charge; the strong charge comes in three types designated by color names (red, green, blue). Particles or combinations of particles can be neutral to the electromagnetic, weak or strong interaction, but not to the gravitational interaction. For instance, electrons have electric and weak charges but no color charge, and atoms are electrically neutral. At astrophysical scales, the dominant interaction is gravita- tion; at atomic scales, O(1nm), it is the electromagnetic interaction; and at the scale of nuclei, O(1fm), it is the strong interaction.
- 40. 8 1 Understanding the Universe: Cosmology, Astrophysics, Particles… In quantum physics the vacuum is not empty at all. Heisenberg’s uncertainty relations allow energy conservation violations by a quantity ∆E within small time intervals ∆t such that ∆t ≃ /∆E. Massive particles that live in such tiny time intervals are called “virtual.” But, besides these particles which are at the origin of measurable effects (like the Casimir effect, see Chap.6), we have just discovered that space is filled by an extra field to which is associated the Higgs boson, a neutral spinless particle with mass about 125 GeV/c2 . Particles in the present theory are intrinsically massless, and it is their interaction with the Higgs field that originates their mass: the physical properties of particles are related to the properties of the quantum vacuum. 1.3 The Particles of Everyday Life As we have seen, matter around us is essentially made of atoms; these atoms can be explained by just three particles: protons and neutrons (making up the atomic nuclei) and electrons. Electrons are believed to be elementary particles, while protons and neutrons are believed to be triplets of quarks – uud and udd, respectively. Particles madeoftripletsofquarksarecalledbaryons.Electronsandprotonsarestableparticles to the best of our present knowledge, while neutrons have an average lifetime (τ) of about 15min if free, and then they decay, mostly into a proton, an electron and an antineutrino—the so-called β decay. Neutrons in atoms, however, can be stable: the binding energy constraining them in the atomic nucleus can be such that the decay becomes energetically forbidden. Baryons are not the only allowed combination of quarks: notably, mesons are allowed combinations of a quark and an antiquark. All mesons are unstable. The lightest mesons, called pions, are combinations of u and d quarks and their antipar- ticles; they come in a triplet of charge (π+ , π− , π0 ) and have masses of about 0.14 GeV/c2 . Although unstable (τπ± ≃ 26 ns, mostly decaying through π+ → μ+ νμ and similarly for π− ; τπ0 ≃ 10−16 s, mostly decaying through π0 → γγ), pions are also quite common, since they are one of the final products of the chain of interactions of particles coming from the cosmos (cosmic rays, see later) with the Earth’s atmo- sphere. All baryons and mesons (i.e., hadrons) considered up to now are combinations of u and d quarks and of their antiparticles. Strange hadrons (this is the term we use for baryons and mesons involving the s, or strange, quark) are less common, since the mass of the s is larger and the lifetimes of strange particles are of the order of 1 ns. The lightest strange mesons are called the K mesons, which can be charged (K+ , K− ) or neutral; the lightest strange baryon (uds) is called the Λ. The heavier brothers of the electrons, the muons (with masses of about 0.11 GeV/c2 ), are also common, since they have a relatively long lifetime (τμ± ≃ 2.2 µs) and they can propagate for long distances in the atmosphere. They also appear in the chain of interactions/decays of the products of cosmic rays.
- 41. 1.3 The Particles of Everyday Life 9 Last but not least, a “field particle” is fundamental for our everyday life: the quantum of electromagnetic radiation, the photon (γ). The photon is massless to the best of our knowledge, and electrically neutral. Photon energies are related to their wavelength λ through E = hc/λ, and the photons of wavelengths between about 0.4 and 0.7µm can be perceived by our eyes as light. 1.4 The Modern View of Interactions: Quantum Fields and Feynman Diagrams The purpose of physics is to describe (and possibly predict) change with time. A general concept related to change is the concept of interaction, i.e., the action that occurs as two or more objects have an effect upon one another. Scattering and decay are examples of interactions, leading from an initial state to a final state. The concept of interaction is thus a generalization of the concept of force exchange in classical physics. Quantum field theories (QFT), which provide in modern physics the description of interactions, describe nature in terms of fields, i.e., of wavefunctions defined in spacetime. A force between two particles (described by “particle fields”) is described intermsoftheexchangeofvirtualforcecarrierparticles(againdescribedbyappropri- ate fields) between them. For example, the electromagnetic force is mediated by the photon field; weak interactions are mediated by the Z and W± fields, while the medi- ators of the strong interaction are called gluons. “Virtual” means that these particles can be off-shell; i.e., they do not need to have the “right” relationship between mass, momentum, and energy—this is related to the virtual particles that we discussed when introducing the uncertainty relations, which can violate energy–momentum conservation for short times. Feynman diagrams are pictorial representations of interactions, used in particular for interactions involving subatomic particles, introduced by Richard Feynman8 in the late 1940s. The orientation from left to right in a Feynman diagram normally represents time: an interaction process begins on the left and ends on the right. Basic fermions are represented by straight lines with possibly an arrow to the right for particles, and to the left for antiparticles. Force carriers are represented typically by wavy lines 8Richard Feynman (New York 1918–Los Angeles 1988), longtime professor at Caltech, is known for his work in quantum mechanics, in the theory of quantum electrodynamics, as well as in particle physics; he participated in the Manhattan project. In addition, he proposed quantum computing. He received the Nobel Prize in Physics in 1965 for his “fundamental work in quantum electrodynamics, with deep-plowing consequences for the physics of elementary particles.” His life was quite adven- turous, and full of anecdotes. In the divorce file related to his second marriage, his wife complained that “He begins working calculus problems in his head as soon as he awakens. He did calculus while driving in his car, while sitting in the living room, and while lying in bed at night.” He wrote several popular physics books, and an excellent general physics textbook now freely available at http://www.feynmanlectures.caltech.edu/.
- 42. 10 1 Understanding the Universe: Cosmology, Astrophysics, Particles… (photons), springs (gluons), dashed lines (W± and Z). Two important rules that the Feynman diagrams must satisfy clarify the meaning of such representation: • conservation of energy and momentum is required at every vertex; • lines entering or leaving the diagram represent real particles and must have E2 = p2 c2 + m2 c4 (seeinthenextchapterthediscussiononEinstein’sspecialrelativity). Associated with Feynman diagrams are mathematical rules (called the “Feynman rules”) that enable the calculation of the probability (quantum mechanically, the square of the absolute value of the amplitude) for a given reaction to occur; we shall describe the quantitative aspects in larger detail in Chaps.6 and 7. Figure 1.3, left, represents a simple Feynman diagram, in which an electron and a proton are mutually scattered as the result of an electromagnetic interaction (virtual photon exchange) between them. This process requires two vertices in which the photon interacts with the charged particle (one for each particle), and for this kind of scattering this is the minimum number of vertices—we say that this is the representation of the process at leading order. The Feynman rules allow associating to each vertex a multiplication factor con- tributing to the total “amplitude”; the probability of a process is proportional to the square of the amplitude. For example in the case of a photon coupling (two photon vertices) this factor is the “coupling parameter” 1 4πǫ0 e2 c ≃ 1 137 for each photon, so the amplitudes for diagrams with many photons (see for example Fig. 1.3, right) are small, compared to those with only one. Technically, the Feynman rules allow expressing the probability of a process as a power series expansion in the coupling parameter. One can draw all possible diagrams up to some number of mediators of the exchange, depending on the accuracy desired; then compute the amplitude for each diagram following the Feynman rules, sum all the amplitudes (note that the diagrams could display negative interference), and calculate the square of the modulus of the amplitude, which will give the probability. This perturbative technique is only of practical use when the coupling parameter is small, that is, as we shall see, for electromagnetic or weak interactions, but not for strong interactions, except at very high energies (the coupling parameter of strong interactions decreases with energy). 1.5 A Quick Look at the Universe The origin and destiny of the Universe are, for most researchers, the fundamen- tal question. Many answers were provided over the ages, a few of them built over scientific observations and reasoning. Over the last century enormous scientific theo- retical and experimental breakthroughs have occurred: less than a century ago, people
- 43. 1.5 A Quick Look at the Universe 11 Fig. 1.3 Electromagnetic scattering: interaction between an electron and a proton. Left: via the exchange of one virtual photon. Right: the same process with one more virtual photon—the ampli- tude decreases by a factor of approximately 1/137 believed that the Milky Way, our own galaxy, was the only galaxy in the Universe; now we know that there are 1011 galaxies within the observable universe, each con- taining some 1011 stars. Most of them are so far away that we cannot even hope to explore them. Let us start an imaginary trip across the Universe from the Earth. The Earth, which has a radius of about 6400km, is one of the planets orbiting around the Sun (we shall often identify the Sun with the symbol ⊙, which comes from its hieroglyphic representation). The latter is a star with a mass of about 2 × 1030 kg located at a distance from us of about 150 million km (i.e., 500 light seconds). We call the average Earth–Sun distance the astronomical unit, in short AU or au. The ensemble of planets orbiting the Sun is called the solar system. Looking to the aphelion of the orbit of the farthest acknowledged planet, Neptune, the solar system has a diameter of 9 billion km (about 10 light hours, or 60 AU). The Milky Way (Fig.1.4) is the galaxy that contains our solar system. Its name “milky” is derived from its appearance as a dim glowing band arching across the night sky in which the naked eye cannot distinguish individual stars. The ancient Romans named it “via lactea,” which literally corresponds to the present name (being lac the latin word for milk)—the term “galaxy,” too, descends from a Greek word indicating milk. Seen from Earth with the unaided eye, the Milky Way appears as a band because its disk-shaped structure is viewed edge-on from the periphery of the galaxy itself. Galilei9 first resolved such band of light into individual stars with his telescope, in 1610. 9Galileo Galilei (1564–1642) was an Italian physicist, mathematician, astronomer, and philosopher who deeply influenced the scientific thought down to the present days. He first formulated some of the fundamental laws of mechanics, like the principle of inertia and the law of accelerated motion; he formally proposed, with some influence from previous works by Giordano Bruno, the principle of relativity. Galilei was professor in Padua, nominated by the Republic of Venezia, and astronomer in Firenze. He built the first practical telescope (using lenses) and using this instrument he could perform astronomical observations which supported Copernicanism; in particular he discovered the phases of Venus, the four largest satellites of Jupiter (named the Galilean moons in his honor), and he observed and analyzed sunspots. Galilei also made major discoveries in military science
- 44. 12 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.4 The Milky Way seen from top and from side. From https://courses.lumenlearning.com/ astronomy The Milky Way is a spiral galaxy some 100 000 light-years (ly) across, 1000 ly to 2000 ly thick, with the solar system located within the disk, about 30 000 ly away from the galactic center in the so-called Orion arm. The stars in the inner 10 000 ly form a bulge and a few bars that radiate from the bulge. The very center of the galaxy, in the constellation of Sagittarius, hosts a supermassive black hole of some 4 million solar masses, as determined by studying the orbits of nearby stars. The interstellar medium (ISM) is filled by partly ionized gas, dust, and cosmic rays, and it accounts for some 15% of the total mass of the disk. The gas is inhomogeneously distributed and it is mostly confined to discrete clouds occupying a few percent of the volume. A magnetic field of a few µG interacts with the ISM. With its ∼1011 stars, the Milky Way is a relatively large galaxy. Teaming up with a similar-sized partner (called the Andromeda galaxy), it has gravitationally trapped many smaller galaxies: together, they all constitute the so-called Local Group. The Local Group comprises more than 50 galaxies, including numerous dwarf galaxies— some are just spherical collections of hundreds of stars that are called globular clus- ters. Its gravitational center is located somewhere between the Milky Way and the Andromeda galaxies. The Local Group covers a diameter of 10 million light-years, or 10 Mly (i.e., 3.1 megaparsec,10 Mpc); it has a total mass of about 1012 solar masses. and technology. He came into conflict with the Catholic Church, for his support of Copernican theories. In 1616 the Inquisition declared heliocentrism to be heretical, and Galilei was ordered to refrain from teaching heliocentric ideas. Galilei argued that tides were an additional evidence for the motion of the Earth. In 1633 the Roman Inquisition found Galilei suspect of heresy, sentencing him to indefinite imprisonment; he was kept under house arrest in Arcetri, near Florence, until his death. 10The parsec (symbol: pc, and meaning “parallax of one arcsecond”) is often used in astronomy to measure distances to objects outside the solar system. It is defined as the length of the longer leg of
- 45. 1.5 A Quick Look at the Universe 13 Fig. 1.5 Redshift of emission spectrum of stars and galaxies at different distances. A star in our galaxy is shown at the bottom left with its spectrum on the bottom right. The spectrum shows the dark absorption lines, which can be used to identify the chemical elements involved. The other three spectra and pictures from bottom to top show a nearby galaxy, a medium distance galaxy, and a distant galaxy. Using the redshift we can calculate the relative radial velocity between these objects and the Earth. From http://www.indiana.edu Galaxies are not uniformly distributed; most of them are arranged into groups (containing some dozens of galaxies) and clusters (up to several thousand galaxies); groups and clusters and additional isolated galaxies form even larger structures called superclusters that may span up to 100 Mly. This is how far our observations can go. In 1929 the American astronomer Edwin Hubble, studying the emission of radi- ation from galaxies, compared their speed (calculated from the Doppler shift of their emission lines) with the distance (Fig.1.5), and discovered that objects in the Universe move away from us with velocity v = H0d , (1.1) where d is the distance to the object, and H0 is a parameter called the Hubble constant (whose value is known today to be about 68kms−1 Mpc−1 , i.e., 21kms−1 Mly−1 ). The above relation is called Hubble’s law (Fig.1.6). Note that at that time galaxies beyond the Milky Way had just been discovered. The Hubble law means that sources at cosmological distances (where local motions, often resulting from galaxies being in gravitationally bound states, are negligible) are observed to move away at speeds that are proportionally higher for larger distances. The Hubble constant describes the rate of increase of recession velocities for increasing distance. The Doppler redshift a right triangle, whose shorter leg corresponds to one astronomical unit, and the subtended angle of the vertex opposite to that leg is one arcsecond. It corresponds to approximately 3 ×1016 m, or about 3.26 light-years. Proxima Centauri, the nearest star, is about 1.3 pc from the Sun.
- 46. 14 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.6 Experimental plot of the relative velocity (in km/s) of known astrophysical objects as a function of distance from Earth (in Mpc). Several methods are used to determine the distances. Distances up to hundreds of parsecs are measured using stellar parallax (i.e., the difference between the angular positions from the Earth with a time difference of 6 months). Distances up to 50 Mpc are measured using Cepheids, i.e., periodically pulsating stars for which the luminosity is related to the pulsation period (the distance can thus be inferred by comparing the intrinsic luminosity with the apparent luminosity). Finally, distances from 1 to 1000 Mpc can be measured with another type of standard candle, Type Ia supernova, a class of remnants of imploded stars. From 15 to 200 Mpc, the Tully–Fisher relation, an empirical relationship between the intrinsic luminosity of a spiral galaxy and the width of its emission lines (a measure of its rotation velocity), can be used. The methods, having large superposition regions, can be cross-calibrated. The line is a Hubble law fit to the data. From A. G. Riess, W. H. Press and R. P. Kirshner, Astrophys. J. 473 (1996) 88 z = λ′ λ − 1 can thus also be used as a metric of the distance of objects. To give an idea of what H0 means, the speed of revolution of the Earth around the Sun is about 30km/s. Andromeda, the large galaxy closest to the Milky Way, is at a distance of about 2.5 Mly from us—however we and Andromeda are indeed approaching: this is an example of the effect of local motions. Dimensionally, we note that H0 is the inverse of a time: H0 ≃ (14 × 109 years)−1 . A simple interpretation of the Hubble law is that, if the Universe had always been expanding at a constant rate, about 14 billion years ago its volume was zero—naively, we can think that it exploded through a quantum singularity, such an explosion being usually called the “Big Bang.” This age is consistent with present estimates of the age of the Universe within gravitational theories, which we shall discuss later in this book, and slightly larger than the age of the oldest stars, which can be measured from the presence of heavy nuclei. The picture looks consistent.
- 47. 1.5 A Quick Look at the Universe 15 The adiabatic expansion of the Universe entails a freezing with expansion, which in the nowadays quiet Universe can be summarized as a law for the evolution of the temperature T with the size R, T ∝ 1 R(t) . The present temperature is slightly less than 3 K and can be measured from the spectrum of the blackbody (microwave) radiation (the so-called cosmic microwave background, or CMB, permeating the Universe). The formula implies also that study- ing the ancient Universe in some sense means exploring the high-energy world: subatomic physics and astrophysics are naturally connected. Tiny quantum fluctuations in the distribution of cosmic energy at epochs corre- sponding to fractions of a second after the Big Bang led to galaxy formation. Density fluctuations grew with time into proto-structures which, after accreting enough mass from their surroundings, overcame the pull of the expanding universe and after the end of an initial era dominated by radiation collapsed into bound, stable structures. The average density of such structures was reminiscent of the average density of the Universe when they broke away from the Hubble expansion: so, earlier-forming structures have a higher mean density than later-forming structures. Proto-galaxies were initially dark. Only later, when enough gas had fallen into their potential well, stars started to form—again, by gravitational instability in the gas—and shine due to the nuclear fusion processes activated by the high temperatures caused by gravita- tional forces. The big picture of the process of galaxy formation is probably under- stood by now, but the details are not. The morphological difference between disk (i.e., spiral) galaxies and spheroidal (i.e., elliptical) galaxies are interpreted as due to the competition between the characteristic timescale of the infall of gas into the protogalaxy’s gravitational well and the timescale of star formation: if the latter is shorter than the former, a spheroidal (i.e., three-dimensional) galaxy likely forms; if it is longer, a disk (i.e., two-dimensional) galaxy forms. A disk galaxy is rotation supported, whereas a spheroidal galaxy is pressure supported—stars behaving in this case like gas molecules. It is conjectured that the velocity dispersion (∼200km/s) among proto-galaxies in the early Universe may have triggered rotation motions in disk galaxies, randomly among galaxies but orderly within individual galaxies. Stars also formed by gravitational instabilities of the gas. For given conditions of density and temperature, gas (mostly hydrogen and helium) clouds collapse and, if their mass is suitable, eventually form stars. Stellar masses are limited by the conditions that (i) nuclear reactions can switch on in the stellar core (0.1 solar masses), and (ii) the radiation drag of the produced luminosity on the plasma does not disrupt the star’s structure (100 solar masses). For a star of the mass of the Sun, formation takes 50 million years—the total lifetime is about 11 billion years before collapsing to a “white dwarf,” and in the case of our Sun some 4.5 billion years are already gone. Stars span a wide range of luminosities and colors and can be classified according to these characteristics. The smallest stars, known as red dwarfs, may contain as little as 10% the mass of the Sun and emit only 0.01% as much energy, having typical
- 48. 16 1 Understanding the Universe: Cosmology, Astrophysics, Particles… surface temperatures of 3000 K, i.e., roughly half the surface temperature of the Sun. Red dwarfs are by far the most numerous stars in the Universe and have lifetimes of tens of billions of years, much larger than the age of the Universe. On the other hand, the most massive stars, known as hypergiants, may be 100 or more times more massive than the Sun, and have surface temperatures of more than 40 000K. Hypergiants emit hundreds of thousands of times more energy than the Sun, but have lifetimes of only a few million years. They are thus extremely rare today and the Milky Way contains only a handful of them. Luminosity,11 radius and temperature of a star are in general linked. In a temperature-luminosity plane, most stars populate a locus that can be described (in log scale) as a straight line (Fig. 1.7): this is called the main sequence. Our Sun is also found there—corresponding to very average temperature and luminosity. The fate of a star depends on its mass. The heavier the star, the larger its gravita- tional energy, and the more effective are the nuclear processes powering it. In average stars like the Sun, the outer layers are supported against gravity until the stellar core stops producing fusion energy; then the star collapses as a “white dwarf”—an Earth- sized object. Main-sequence stars over 8 solar masses can die in a very energetic explosion called a (core-collapse, or Type II) supernova. In a supernova, the star’s core, made of iron (which being the most stable atom, i.e., one whose mass defect per nucleon is maximum, is the endpoint of nuclear fusion processes, Fig.1.8) col- lapses and the released gravitational energy goes on heating the overlying mass layers which, in an attempt to dissipate the sudden excess heat by increasing the star’s radi- ating surface, expand at high speed (10 000km/s and more) to the point that the star gets quickly disrupted—i.e., explodes. Supernovae release an enormous amount of energy, about 1046 J—mostly in neutrinos from the nuclear processes occurring in the core, and just 1% in kinetic energies of the ejecta—in a few tens of seconds.12 For a period of days to weeks, a supernova may outshine its entire host galaxy. Being the 11The brightness of a star at an effective wavelength λ as seen by an observer on Earth is given by its apparent magnitude. This scale originates in the Hellenistic practice of dividing stars into six magnitudes: the brightest stars were said to be of first magnitude (m = 1), while the faintest were of sixth magnitude (m = 6), the limit of naked eye human visibility. The system is today formalized by defining a first magnitude star as a star that is 100 times as bright as a sixth magnitude star; thus, a first magnitude star is 5 √ 100 (about 2.512) times as bright as a second magnitude star (obviously the brighter an object appears, the lower the value of its magnitude). The stars Arcturus and Vega have an apparent magnitude approximately equal to 0. The absolute magnitude MV is defined to be the visual (λ ∼ 550 nm) apparent magnitude that the object would have if it were viewed from a distance of 10 parsec, in the absence of light extinction; it is thus a measure of the luminosity of an object. The problem of the relation between apparent magnitude, absolute magnitude, and distance is related also to cosmology, as discussed in Chap.8. The absolute magnitude is nontrivially related to the bolometric luminosity, i.e., to the total electromagnetic power emitted by a source; the relation is complicated by the fact that only part of the emission spectrum is observed in a photometric band. The absolute magnitude of the Sun is MV, ⊙ ≃ 4.86, and its absolute bolometric magnitude is Mbol, ⊙ ≃ 4.76; the difference MV -Mbol (for the Sun, MV, ⊙- Mbol, ⊙ ≃ 0.1) is called the bolometric correction BC, which is a function of the temperature. It can be approximated as BC(T) ≃ 29500/T + 10 log10 T − 42.62. 12Note that frequently astrophysicist use as a unit of energy the old “cgs” (centimeter–gram–second) unit called erg; 1 erg = 10−7 J.
- 49. 1.5 A Quick Look at the Universe 17 Fig. 1.7 Hertzsprung–Russell diagram plotting the luminosities of stars versus their stellar classi- fication or effective temperature (color). From http://www.atnf.csiro.au/outreach/education energy of the explosion large enough to generate hadronic interactions, basically any element and many subatomic particles are produced in these explosions. On average, in a typical galaxy (e.g., the Milky Way) supernova explosions occur just once or twice per century. Supernovae leave behind neutron stars or black holes.13 The heavier the star, the more effective the fusion process, and the shorter the lifetime. We need a star like our Sun, having a lifetime of a few tens of billion of years, to both give enough time to life to develop and to guarantee high enough temperatures for humans. The solar system is estimated to be some 4.6 billion years old and to have started from a molecular cloud. Most of the collapsing mass collected in the center, forming the Sun, while the rest flattened into a disk out of which the planets formed. The Sun is too young to have created heavy elements in such an abundance to justify carbon-based life on Earth. The carbon, nitrogen, and oxygen atoms in our bodies, as well as atoms of all other heavy elements, were created in previous generations of stars somewhere in the Universe. 13The Chandrasekhar limit is the maximum mass theoretically possible for a star to end its lifecycle into a dwarf star: Chandrasekhar in 1930 demonstrated that it is impossible for a collapsed star to be stable if its mass is greater than ∼1.44 times the mass of the Sun. Above 1.5–3 solar masses (the limit is not known, depending on the initial conditions) a star ends its nuclear-burning lifetime into a black hole. In the intermediate range it will become a neutron star.
- 50. 18 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.8 Binding energy per nucleon for stable atoms. Iron (56Fe) is the stable element for which the binding energy per nucleon is the largest (about 8.8 MeV); it is thus the natural endpoint of processes of fusion of lighter elements, and of fission of heavier elements (although 58Fe and 56Ni have a slightly higher binding energy, by less than 0.05%, they are subject to nuclear photodisintegration). From http://hyperphysics.phy-astr.gsu.edu Fig. 1.9 Present energy budget of the Universe Dark Matter 26% Atoms 5% Dark Energy 69% The study of stellar motions in galaxies indicates the presence of a large amount of unseen mass in the Universe. This mass seems to be of a kind presently unknown to us; it neither emits nor absorbs electromagnetic radiation (including visible light) at any significant level. We call it dark matter: its abundance in the Universe amounts to an order of magnitude more than the conventional matter we are made of. Dark matter represents one of the greatest current mysteries of astroparticle physics. Indications exist also of a further form of energy, which we call dark energy. Dark energy contributes to the total energy budget of the Universe three times more than dark matter.
- 51. 1.5 A Quick Look at the Universe 19 The fate of the Universe depends on its energy content. In the crude approximation of a homogeneous and isotropic Universe with a flat geometry, the escape velocity vesc of an astrophysical object of mass m at a distance r from a given point can be computed from the relation mv2 esc 2 − GM m r = mv2 esc 2 − G 4 3 πr3 ρ c2 m r = 0 =⇒ vesc = 8 3 πGr2 ρ c2 , where M = 4 3 πr3 ρ/c2 is the amount of mass in the sphere of radius r, ρ being the average energy density, and G the gravitational constant. Given Hubble’s law, if v = H0r vesc = 8 3 πGr2 ρ c2 =⇒ ρ ρcrit = 3H2 0 c2 8πG the Universe will eventually recollapse, otherwise it will expand forever. ρcrit, about 5 GeV/m3 , is called the critical energy density of the Universe. In summary, we live in a world that is mostly unknown even from the point of view of the nature of its main constituents (Fig.1.9). The evolution of the Universe and our everyday life depend on this unknown external world. First of all, the ultimate destiny of the Universe—a perpetual expansion or a recollapse—depends on the amount of all the matter in the Universe. Moreover, every second, high-energy particles (i.e., above 1 GeV) of extraterrestrial origin pass through each square centimeter on the Earth, and they are messengers from regions where highly energetic phenomena take place that we cannot directly explore. These are the so-called cosmic rays, discovered in the beginning of the nineteenth century (see Chap.3). It is natural to try to use these messengers in order to obtain information on the highest energy events occurring in the Universe. 1.6 Cosmic Rays The distribution in energy (the so-called energy spectrum) of cosmic rays14 is quite well described by a power law E−p with p a positive number (Fig.1.10). The spectral index p is around 3 on average. After the low-energy region dominated by cosmic rays from the Sun (the solar wind), the spectrum becomes steeper for energy values of less than ∼1000 TeV (150 times the maximum energy foreseen for the beams of the LHC collider at CERN): this is the energy region that we know to be dom- inated by cosmic rays produced by astrophysical sources in our Galaxy, the Milky Way. For higher energies a further steepening occurs, the point at which this change of slope takes place being called the “knee.” Some believe that the region above 14In this textbook we define as cosmic rays all particles of extraterrestrial origin. It should be noted that other textbooks instead define as cosmic rays only nuclei, or only protons and ions—i.e., they separate gamma rays and neutrinos from cosmic rays.
- 52. 20 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.10 Energy spectrum (number of incident particles per unit of energy, per second, per unit area, and per unit of solid angle) of the primary cosmic rays. The vertical band on the left indicates the energy region in which the emission from the Sun is supposed to be dominant; the central band the region in which most of the emission is presumably of galactic origin; the band on the right the region of extragalactic origin. By Sven Lafebre (own work) [GFDL http://www.gnu.org/ copyleft/fdl.html], via Wikimedia Commons this energy is dominated by cosmic rays produced by extragalactic sources, mostly supermassive black holes growing at the centers of other galaxies. For even higher energies (more than one million TeV) the cosmic-ray spectrum becomes less steep, resulting in another change of slope, called the “ankle”; some others believe that the knee is caused by a propagation effect, and the threshold for the dominance of extragalactic sources is indeed close to the ankle. Finally, at the highest energies in the figure a drastic suppression is present—as expected from the interaction of long- traveling particles with the cosmic microwave background, remnant of the origin of the Universe.15 The majority of high-energy particles in cosmic rays are protons (hydrogen nuclei); about 10% are helium nuclei (nuclear physicists usually call them alpha par- ticles), and 1% are neutrons or nuclei of heavier elements. Together, these account 15A theoretical upper limit on the energy of cosmic rays from distant sources was computed in 1966 by Greisen, Kuzmin, and Zatsepin, and it is called today the GZK cutoff. Protons with energies above a threshold of about 1020 eV suffer a resonant interaction with the cosmic microwave background photons to produce pions through the formation of a short-lived particle (resonance) called ∆: p + γ → ∆ → N + π. This continues until their energy falls below the production threshold. Because of the mean path associated with the interaction, extragalactic cosmic rays from distances larger than 50 Mpc from the Earth and with energies greater than this threshold energy should be strongly suppressed on Earth, and there are no known sources within this distance that could produce them. A similar effect (nuclear photodisintegration) limits the mean free path for the propagation of nuclei heavier than the proton.
- 53. 1.6 Cosmic Rays 21 for 99% of cosmic rays, and electrons and photons make up the remaining 1%. Note that the composition is expected to vary with energy; given the energy dependence of the flux, however, only the energies below the knee are responsible for this propor- tion. The number of neutrinos is estimated to be comparable to that of high-energy photons, but it is very high at low energies because of the nuclear processes that occur in the Sun: such processes involve a large production of neutrinos. Neutral and stable cosmic messengers (gamma rays, high-energy neutrinos, grav- itational waves) are very precious since they are not deflected by extragalactic (order of 1 nG–1 fG) or by galactic (order of 1 µG) magnetic fields and allow pointing directly to the source. While we detect a large flux of gamma rays and we know sev- eral cosmic production sites, evidence for astrophysical neutrinos and gravitational waves was only recently published, respectively in 2014 and in 2016. Cosmic rays hitting the atmosphere (called primary cosmic rays) generally pro- duce secondary particles that can reach the Earth’s surface, through multiplicative showers. About once per minute, a single subatomic particle enters the Earth’s atmosphere with an energy larger than 10 J. Somewhere in the Universe there are accelerators that can impart to single protons energies 100 million times larger than the energy reached by the most powerful accelerators on Earth. It is thought that the ultimate engine of the acceleration of cosmic rays is gravity. In gigantic gravitational collapses, such as those occurring in supernovae (stars imploding at the end of their lives, see Fig.1.11, left) and in the accretion of supermassive black holes (equivalent to millions to billions of solar masses) at the expense of the surrounding matter (Fig.1.11, right), part of the potential gravitational energy is transformed, through not fully understood mechanisms, into kinetic energy of the particles. The reason why the maximum energy attained by human-made accelerators with the presently known acceleration technologies cannot compete with the still myste- rious cosmic accelerators is simple. The most efficient way to accelerate particles requires their confinement within a radius R by a magnetic field B, and the final energy is proportional to the product R × B. On Earth, it is difficult to imagine rea- sonable confinement radii greater than one hundred kilometers, and magnetic fields stronger than 10T (i.e., one hundred thousand times the Earth’s magnetic field). This combination can provide energies of a few tens of TeV, such as those of the LHC accelerator at CERN. In nature, accelerators with much larger radii exist, such as supernova remnants (light-years) and active galactic nuclei (tens of thousands of light-years). Of course human-made accelerators have important advantages, such as being able to control the flux and the possibility of knowing the initial conditions (cosmic ray researchers do not know a-priori the initial conditions of the phenomena they study). Among cosmic rays, photons are particularly important. As mentioned above, the gamma photons (called gamma rays for historical reasons) are photons of very high energy and occupy the most energetic part of the electromagnetic spectrum; being neutral they can travel long distances without being deflected by galactic and extragalactic magnetic fields; hence, they allow us to directly study their emission sources. These facts are now pushing us to study in particular the high-energy gamma
- 54. 22 1 Understanding the Universe: Cosmology, Astrophysics, Particles… Fig. 1.11 Left: The remnant of the supernova in the Crab region (Crab nebula), a powerful gamma emitter in our Galaxy. The supernova exploded in 1054 and the phenomenon was recorded by Chinese astronomers. Until 2010, most astronomers regarded the Crab as a standard candle for high-energy photon emission, but recently it was discovered that the Crab Nebula from time to time flickers. Anyway, most plots of sensitivity of detectors refer to a “standard Crab” as a reference unit. The vortex around the center is visible; a neutron star rapidly rotating (with a period of around 30 ms) and emitting pulsed gamma-ray streams (pulsar) powers the system. Some supernova remnants, seen from Earth, have an apparent dimension of a few tenths of a degree—about the dimension of the Moon. Right: A supermassive black hole accretes, swallowing neighboring stellar bodies and molecular clouds, and emits jets of charged particles and gamma rays. Credits: NASA rays and cosmic rays of hundreds of millions of TeV. However, gamma rays are less numerous than charged cosmic rays of the same energy, and the energy spectrum of charged cosmic rays is such that particles of hundreds of millions of TeV are very rare. The task of experimental physics is, as usual, challenging, and often discoveries correspond to breakthroughs in detector techniques. A sky map of the emitters of very high-energy photons in galactic coordinates16 is shown in Fig.1.12. One can identify both galactic emitters (in the equatorial plane) 16Usually the planar representations of maps of the Universe are done in galactic coordinates. To understand what this means, let us start from a celestial coordinate system in spherical coordinates, in which the Sun is at the center, the primary direction is the one joining the Sun with the center of the Milky Way, and the galactic plane is the fundamental plane. Coordinates are positive toward North and East in the fundamental plane. We define as galactic longitude (l or λ) the angle between the projection of the object in the galactic plane and the primary direction. Latitude (symbol b or φ) is the angular distance between the object and the galactic plane. For example, the North galactic pole has a latitude of +90◦. Plots in galactic coordinates are then projected onto a plane, typically using an elliptical (Mollweide or Hammer; we shall describe the Mollweide projection here) projection preserving areas. The Mollweide projection transforms latitude and longitude to plane coordinates x and y via the equations (angles are expressed in radians):
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