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Undergraduate Lecture Notes in Physics Forfurthervolumes: www.springer.com/series/8917 UndergraduateLectureNotesinPhysics(ULNP)publishesauthoritativetextscoveringtop- ics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduateinstruction,typicallycontainingpracticeproblems,workedexamples,chapter summaries,andsuggestionsforfurtherreading. ULNPtitlesmustprovideatleastoneofthefollowing: • Anexceptionallyclearandconcisetreatmentofastandardundergraduatesubject. • Asolidundergraduate-levelintroductiontoagraduate,advanced,ornon-standardsubject. • Anovelperspectiveoranunusualapproachtoteachingasubject. ULNPespeciallyencouragesnew,original,andidiosyncraticapproachestophysicsteaching attheundergraduatelevel. ThepurposeofULNPistoprovideintriguing,absorbingbooksthatwillcontinuetobethe reader’spreferredreferencethroughouttheiracademiccareer. Sylvie Braibant (cid:2) Giorgio Giacomelli (cid:2) Maurizio Spurio Particles and Fundamental Interactions: Supplements, Problems and Solutions A Deeper Insight into Particle Physics SylvieBraibant MaurizioSpurio DepartmentofPhysicsandINFN DepartmentofPhysicsandINFN UniversityofBologna UniversityofBologna Bologna,Italy Bologna,Italy GiorgioGiacomelli DepartmentofPhysicsandINFN UniversityofBologna Bologna,Italy ISSN2192-4791 ISSN2192-4805(electronic) UndergraduateLectureNotesinPhysics ISBN978-94-007-4134-8 ISBN978-94-007-4135-5(eBook) DOI10.1007/978-94-007-4135-5 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2012936363 ©SpringerScience+BusinessMediaDordrecht2012 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface TheProblemspresentedhererefertothetopicsdiscussedinthecorresponding14 chapters of the Particles and Fundamental Interactions textbook. This Problems, Solutions and Supplements book is aimed at students in a course of Experimental Particle Physics, not only as a preparation for a written examination, but also as a necessaryinstrumentforadeeperunderstandingofhighenergyphysics.Itcontains 170 problems of different difficulty levels. Some of them are traditional, covering mostaspectsofparticlepropertiesandoftheirfundamentalinteractions,andsome are more advanced. Some problems are derived from our teaching experience to undergraduate students; some are derived from the admission examination to the PhDcoursesinItalianuniversities;somearecompletelyoriginal,fromourresearch activities. Each problem has an identification number and a title to facilitate the identification of the subject discussed in the text. Most problems are solved step-by-step, to help both students and teachers to get better acquainted to topics presented in the textbook. We follow the same chapter numeration of the textbook. To avoid confusionwhenwerefertochapters,equations,figuresandtablesofParticlesand FundamentalInteractions,thereferenceisenclosedinabox.Inthisway,Fig.7.2 refers to a figure in this manual, and Fig.7.2 to a figure in the textbook. As a general advice, it is useful to try to solve problems only after a first reading of a book.Beforefacingthemoreadvancedproblems,wesuggesttoreadatleastupto Chap.8ofParticlesandFundamentalInteractions,wheretheintroductionofparti- clenomenclatureandclassification,andthepresentationoffundamentalaspectsof theinteractionsarecompleted. In addition to problems and solutions, additional material is presented in form offifteenSupplements.Fourofthempresentthemostpowerfulaccelerators,those which produce cosmic rays. Cosmic rays were of fundamental importance for the discoveryofmostlong-livingparticles,thedevelopmentofparticlephysicsandthat of astroparticle physics. Three Supplements are devoted to the electronic signals, todataacquisitionsystems,totheelectroniclogicsandtriggersoftheexperimental apparatuses,endingwiththecomputingeffortrequiredfortheLHCcollider.These issuesplayalsoakeyroleinthecontributionthatparticlephysicsresearchprovides v vi Preface asaspin-offtechnology.Thisisalsotrueforotherfoursupplements,presentingad- ditionalinformationoninteractionsbetweenchargedparticlesandmatter(multiple Coulombscattering,synchrotronradiation)ortheuseofradioactivedecaysfordat- ingoldobjects.Someproblemscontain,afterthesolutions,somecommentsrelated to past, running or future experiments (as for instance that for the neutrino beams andneutrinooscillations,thesearchforprotondecay,thestudyofsymmetryviola- tionthroughtheelectricdipolemomentoftheneutron,themeasurementofα ,the S studyofastrophysicalobjectsusingchargedparticlesand/orneutrinos,etc.). Wethankmanycolleagues,inparticularthoseoftheformerOPALandMACRO groups(now,CMS,OPERAandANTARES)attheUniversityofBologna,fortheir cooperation. Finally, we are grateful to many students for their suggestions and questionsthatallowedustopreparethisworkinawaythatwehopewillbeuseful formany. Weareresponsiblefortheerrorswhichinevitablycouldbepresentinthisman- ual.Someproblemscontainapproximations,ormaybesolvedindifferentormore straightforwardway.Weapologizeinadvanceforanymistakethatcouldhavesur- vivedandthatthereaderswilldiscover:youarekindlyencouragedtoinformus. Bologna,Italy SylvieBraibant GiorgioGiacomelli MaurizioSpurio Contents 1 HistoricalNotesandFundamentalConcepts . . . . . . . . . . . . . . 1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Supplement1.1:CosmicRaysandAstroparticlePhysics . . . . . . . . . 3 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 ParticleInteractionswithMatterandDetectors . . . . . . . . . . . . 9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Supplement2.1:MultipleScatteringatSmallAngles . . . . . . . . . . . 11 Supplement2.2:MuonEnergyLossatHighEnergies . . . . . . . . . . 12 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 ParticleAcceleratorsandParticleDetection . . . . . . . . . . . . . . 19 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Supplement3.1:SynchrotronRadiation . . . . . . . . . . . . . . . . . . 24 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4 TheParadigmofInteractions:TheElectromagneticCase . . . . . . 37 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Supplement4.1:RadiocarbonDating . . . . . . . . . . . . . . . . . . . 40 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5 FirstDiscussionoftheOtherFundamentalInteractions . . . . . . . 49 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Supplement5.1:BaryonNumberConservation:theSearchforProton Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 vii viii Contents 6 InvarianceandConservationPrinciples . . . . . . . . . . . . . . . . 59 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 InteractionsofHadronsatLowEnergiesandtheStaticQuarkModel 65 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Supplement 7.1: Sum of Angular Momentum and Isospin: theClebsch–GordanCoefficients . . . . . . . . . . . . . . . . . . 68 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8 WeakInteractionsandNeutrinos . . . . . . . . . . . . . . . . . . . . 81 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Supplement8.1:Signals,DataTransmissionandElectronics . . . . . . . 86 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 9 DiscoveriesinElectron–PositronCollisions . . . . . . . . . . . . . . 103 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Supplement9.1:ElectronicLogicandTrigger . . . . . . . . . . . . . . 104 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 10 HighEnergyInteractionsandtheDynamicQuarkModel . . . . . . 113 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Supplement10.1:TheComputingEffortattheLHCCollider . . . . . . 116 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 11 TheStandardModeloftheMicrocosm . . . . . . . . . . . . . . . . . 125 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 12 CP-ViolationandParticleOscillations . . . . . . . . . . . . . . . . . 129 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Supplement12.1:AnalogyfortheNeutrinoMixing . . . . . . . . . . . 132 Supplement12.2:DiracorMajoranaNeutrinos:theDoubleβ Decay . . 133 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 13 MicrocosmandMacrocosm . . . . . . . . . . . . . . . . . . . . . . . 145 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Supplement13.1:CosmicAccelerators . . . . . . . . . . . . . . . . . . 148 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 14 FundamentalAspectsofNucleonInteractions . . . . . . . . . . . . . 163 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Supplement 14.1: Nuclear Collisions of Cosmic Rays During PropagationintheGalaxy . . . . . . . . . . . . . . . . . . . . . . 167 Contents ix Supplement14.2:QuantumMechanicsandNuclearPhysics→White DwarfsandNeutronStars . . . . . . . . . . . . . . . . . . . . . . 171 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183