Selected Exercises in Particle and Nuclear Physics

374 Pages·2018·6.243 MB·English

by  Lorenzo Bianchini (auth.)

UNITEXT for Physics
Lorenzo Bianchini
Selected
Exercises in
Particle and
Nuclear Physics
UNITEXT for Physics
Series editors
Michele Cini, Roma, Italy
Attilio Ferrari, Torino, Italy
Stefano Forte, Milano, Italy
Guido Montagna, Pavia, Italy
Oreste Nicrosini, Pavia, Italy
Luca Peliti, Napoli, Italy
Alberto Rotondi, Pavia, Italy
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Nicola Manini, Milano, Italy
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Lorenzo Bianchini
Selected Exercises in Particle
and Nuclear Physics
123
Lorenzo Bianchini
Italian Institute for Nuclear Physics
Pisa
Italy
ISSN 2198-7882 ISSN 2198-7890 (electronic)
UNITEXTfor Physics
ISBN978-3-319-70493-7 ISBN978-3-319-70494-4 (eBook)
https://doi.org/10.1007/978-3-319-70494-4
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To my wife Elisabetta,
1 Gv 4, 16
Preface
The realm of particle physics is vast: multidisciplinary knowledge across several
domains of physics and mathematics is required to understand the reactions that
occur when particles collideandtomaster thefunctioning oftheexperimentsbuilt
to study these reactions: classical and quantum mechanics, special relativity,
electrodynamics,thermodynamics,chemistry,atomicandnuclearphysics,quantum
fieldtheory,electronics,analysis,geometry,grouptheory,probability,informatics,
among the others. Large-scale particle experiments, like those hosted in the main
laboratories around the world, are perhaps the best example of how multidisci-
plinary this field can become: the successful operation of these complex structures
relies on the synergetic work of hundreds of scientists and engineers; it is only the
combination of their individual expertise that makes it possible to cover all the
needs.
Thanks to the maturity of this field (more than one hundred years old!), a huge
collectionoftextbooks,topicalschools,academicclasses,andscientificliteratureis
available, where both the theoretical and experimental foundations of particle
physics can be elucidated to the desired level of detail. Yet, as for all the other
domainsofphysics,particlephysicsshouldbemoreaboutsolvingproblemsrather
than knowing concepts! The path towards a solid understanding of this discipline
passes through the capability of solving exercises. This book collects a sample of
about 240 solved problems about particle physics in general. About half of the
exercises are drawn from the public exams that have been proposed by the Italian
National Institute for Nuclear research (INFN) to select its scientific staff over the
last decade. Additional material inspired by my personal experience as an under-
graduate student at Scuola Normale Superiore di Pisa, researcher in the CMS
experiment, and teaching assistant at ETH Zürich complements the selection.
Throughout this book, the main emphasis is put on experimental problems,
although some more theoretical ones are also included. Thus, this book is mostly
addressed to experimentalists.
Theproposedexercisesspanseveralsubjectsinparticlephysics,althoughImust
acknowledge that it has not been possible to be truly exhaustive. Several topics
have been unfortunately, yet necessarily, discarded or only marginally mentioned.
vii
viii Preface
In particular, cosmology, dark matter, beyond-standard model theories will not be
much discussed here. Also,apersonalcultural bias towards anLHC-centric vision
of the field may have driven the focus towards the high-energy frontier at the
expenses of other equally lively sectors of research, like neutrino physics, rare
decays, hadron spectroscopy, B physics. Much attention is devoted to the opera-
tional principles of particle detectors, from the more classical ones to the more
recenttechnologies.Particledetectorscannotbeunderstoodwithoutfirstmastering
the basics of the interaction between particles and matter, which therefore repre-
sents another topic of foremost interest. Given that particle detectors typically
provide electric outputs, which need to be processed, stored, and cleaned from the
noise,electronics,informatics,anddataanalysisenternaturallyintothegame,anda
basicknowledgeofbothsubjectsisthereforerequired.Furthermore,anexperiment
in particle physics usually starts by scattering particles: acceleration of particles in
stable and repeatable beams is therefore another important topic. Finally, a proper
scientificmaturitydemandsalsoanoverallpictureofthefield:whatisknown,what
isstillunknownbutimportanttostudy,whatarethetechnologiesathand,andwhat
thefuture lines ofresearch. Several exercisesgo along this direction by discussing
the state of the art on the field, including ongoing or planned measurements and
new experimental techniques.
Theexercisesaregroupedbysubjectintofivechapters,wherethemaintopicof
discussion is first introduced in an academic fashion. Within each chapter, the
exercises are organised as much as possible according to a logical order, so that
each exercise can be propaedeutic to those that follow. Some of the exercises are
used as prototypes for a class of problems. In this case, the relevant concepts and
the general-purpose formulas are derived once and recalled afterwards by pointing
to the master exercise. Other exercises are instead chosen to introduce a particular
topic, which is then explained in some more detail by dedicated mini-lectures.
Referencestothescientificliteratureandtopicaltextbooksarethenprovidedtohelp
the reader go into the various subjects in greater detail. Consistency of notation
throughoutthetextispursuedtoreduceataminimumtheconfusionintroducedby
the abundance of acronyms and conventional symbols peculiar to this field. Some
exercises require a few lines of calculations, others one or more pages. Whenever
possible, one should always try to derive the symbolic solution analytically and
carry out the numerical computation without the help of pocket calculators, as to
train one's capability to handle simple calculations using approximations or
order-of-magnitude estimates. Indeed, experience teaches that there exist a few
constants and formulas that are really worth keeping in mind! In other situations,
one should better rely on computers rather than try the analytical approach. In the
latter case, examples of simple computer routines written in open-source pro-
gramming languages are also proposed.
Per aspera ad astra: solving problems is the most difficult and painful task for
students,butalsoonethatunveilsthetruedegreeofcomprehensionofthesubject.
We hope that this book can serve as supporting material to back up existing and
more complete textbooks on experimental and theoretical particle physics. At the
same time, it should provide a test bench for undergraduate students and young
Preface ix
researchers to validate their level of preparation and hopefully stimulate their
curiosity on the field.
I am much indebted to INFN for allowing me to profit from a large number
of the exercises contained in this book. The richness and variety of topics covered
inthisimmensereservoirofknowledgehavebeenfundamentaltoshapethiswork.
I also want to heartily thank the Institute for Particle Physics of ETH Zürich for
grantingmethetimetoworkonthisbookandforthefantasticteachingexperience
I enjoyed amid its brilliant and lively students.
Pisa, Italy Lorenzo Bianchini
September 2017
Contents
1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Center-of-Mass Dynamics and Particle Decays. . . . . . . . . . . . . . . 54
1.3 Cross Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2 Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.1 Passage of Particles Through Matter . . . . . . . . . . . . . . . . . . . . . . 107
2.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
2.3 Functioning of Particle Detectors. . . . . . . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
3 Accelerators and Experimental Apparatuses. . . . . . . . . . . . . . . . . . . 177
3.1 Tracking of Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
3.2 Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
3.3 Luminosity and Event Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
4 Statistics in Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
4.1 Elements of Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
4.2 Error Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
4.3 Confidence Intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
5 Subnuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
5.1 Conservation Laws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
5.2 Electroweak and Strong Interactions . . . . . . . . . . . . . . . . . . . . . . 293
5.3 Flavour Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.4 Higgs Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 359
xi