Selected topics in Phenomenology Stefano Moretti Scho ol of Physics and Astronomy Univ ersity of Southampton Southampton SO BJ UK and Particle Physics Departmen t Appleton Lab oratory Rutherford Didcot Oxon OX QX Chilton Foreword The tradition is that this course is given using transparencies unlike the other courses in the scho ol and that the transparen cies are simply repro duced in the pro ceedings This year I have used a mixture of slides and whiteb oard These notes at tempt to combine all the material I used throughout the course and also contain some which I could not treat extensively in the lecture theater In preparing my course I used material from Nigel Glover Mike Seymour and Michael Kramer who course I am preceded me as lecturers of the Phenomenology greatly indebted to them for letting me using it I have also ripp ed o some slides from Gavin Salams talks and presenta tions for some of the QCD topics and from Laura Reina in the case of Higgs physics A sp ecial thank go es to Dan Tovey for letting me use many slides from one of his talks for that very last lecture the day after the scho ol dinner and aftermath The references I have used to prepare the course are collected at the end and should ideally provide a go o d starting p oint for those who want to learn more ab out some of the topics I would like to thank Tim Greenshaw for organising the scho ol so well and for his supp ort throughout Lots of thanks also go to the other lecturers to the tutors and primarily to the students Finally I am grateful to Margaret Evans for all the practical arrangements and for coping with my extreme late ness in preparing these notes I was again the last one Intro duction Kants Critique of Pure Reason as interpreted by Wikip edia Phenomenon Phenomena constitute the world as we ex p erience it as opp osed to the world as it exists inde p endently of our exp eriences thinginthemselv es das cannot according to Kant know ding an sich Humans thingsinthemselves only things as we exp erience them Noumenon Thing in itself Ding an sich is an al legedly unknowable undescribable reality that in some way lies b ehind observed phenomena Noumena are sometimes sp oken of though the very notion of individ uating items in the noumenal world is problematic since the very notions of numb er and individuality are among the categories of the understanding which are supp osed to apply only to phenomena not noumena The concept of Phenomena led to a tradition of philos ophy known as Phenomenology Hegel Heidegger etc which we will ignore here Phenomenon in the general sense stands for any observable event phenomena make up the raw data of science Famous quotes No phenomenon is a phenomenon until it is an observed phenomenon Niels Bohr I will nonetheless discuss Sup ersymmetry My denition of high energy phenomenology Branch of highenergy physics that seeks knowledge by Exploiting the hints and clues available in observable phe nomena aka exp erimental data without any preconception on the theory governing the latter Parametrise theories into a set of observables predictions that can directly b e tested by exp eriment thus conrming or disproving the former Phenomenology bridge b etween theory and exp eriment Outline Intro duction The Standard Mo del Beyond Tests of the Standard Mo del QCD running coupling infrared safety factorisation parton dis tribution functions jet pro duction searches for new physics ElectroWeak EW Physics weak interactions from uni tarity Z lineshap e precision tests W b oson pro duction indirect b oson search for the Higgs Higgs Boson Hunting The Higgs mechanism The Higgs picture The Higgs prole Collider searches Sup ersymmetry SUSY Why sup ersymmetry The hierarchy problem and gauge coupling unication The Minimal Sup ersymmetric Standard Mo del MSSM Indirect searches g Collider searches Epilogue Intro duction Current theoretical framework of particle physics is Standard Mo del SM SM is S U SU U gauge theory with Matter elds s b u d u s c b t quarks R R R R R R d c t L L L e e leptons R R R e L L L Force elds W Z g Vector b osons and a Higgs scalar H Q Why do we b elieve in the Standard Mo del A Because conrmed by exp eriment Q Why lo ok Beyond the Standard Mo del BSM A Because SM lacks explanation of fundamental quantities SM Flaws SM do es not explain quantum numb ers EM charge weak isospin hyp ercharge and colour Contains at least arbitrary parameters gauge couplings CPviolating vacuum angle quark masses charged lepton masses weak mixing angles CPviolating CKM phase W mass Higgs mass and p ossibly more parameters in the neutrino sector neutrino masses neutrino mixing angles CPviolating phases More crucially it do es not incorp orate gravity Beyond the Standard Mo del Three kind of problems Mass What is the origin of particle masses Are the masses due to a Higgs b oson What sets the scale of fermion masses Unication Is there a theory unifying all particle interactions Flavour Why are there so many typ es of quarks and leptons What is the origin of CPviolation gravity spacetime originstructure Solutions should incorp orate String theory b est only candidate but not yet predictive Sup ersymmetry SUSY to play a role in solving problems Gauge coupling unication b est with light sparticles Mass hierarchy needs light sparticles for stabilisation SUSY seems essential for the consistency of string theory Jargon a sparticle is a SUSY particle What New Physics NP Which way to go ab out Come up with theory devise mo del for it get out pre dictions compare with exp eriment e theory b elow some high scale Treat SM as eectiv NP describ ed by op erators of dimension suppressed E relevant energy by p owers of E Historic example Fermis theory of weak interactions e decay describ ed by eective Lagrangian e G F p L e e From exp eriment G Fermi coupling GeV F As M W app ears as deviations from eective theory W e e µ = ¦ Ï e e Hence precision tests of the SM can reveal NP Crucial question for phenomenology is What is the scale of new physics TeV Higher We do not know for sure so we push up collider energies Test of the SM QCD Outline Imp ortance of QCD The QCD coupling e hadrons e Infrared safe quantities Jets Parton shower Hadronisation Deeply inelastic scattering HadronHadron collisions New physics searches Imp ortance of QCD QCD is the correct theory of strong interactions in the describ ed sense of a lowenergy eective theory ! Why QCD studies A Quantum Field Theory QFT with unique features asymptotic freedom infrared slavery connement We need to understand QCD also to search for NP for new particles hadropro duction Tevatron and LHC to predict the SM backgrounds to NP signals QCD degrees of freedom quarks gluons aka partons Will study their interactions in e e e p pp and pp See Nicks course for Lagrangian Feynman rules The QCD Lagrangian is given by X A A L F F iD m q q ab b a avours L L host gaugexing g A where F is the eld strength tensor derived from the gluon a eld A A A A AB C B g f A A F A A B C run over the eight colour degrees of and the indices A freedom of the gluon eld The quark elds q are in the a triplet representation of the SU colour group and D is the covariant derivative c c ig t D A ab ab ab The t are matrices in the fundamental representation of SU and satisfy A B AB C C t t if t For a discussion of the gaugexing and ghost terms of the QCD Lagrangian see Nicks course The Feynman rules can b e derived from the QCD La grangian p p i A p B AB g 2 2 p i p i i A p B AB 2 p i i i p b j a ab 6 p m i i j h B AB C g f g p q q g q r i g r p p r all momenta incoming A C A B 2 X AC XBD g g g g ig f f 2 X AD XBC ig f f g g g g 2 X AB XCD ig f f g g g g C D A AB C g f q R q B C A A ig t j i cb R b i c j ß ÌÝÔ e×eØ bÝ FÓiÐÌ X ß ½7 E AB A B AB 1 Tr(t t ) = TR δ , TR = 2 N2 − A A c 1 4 A tabtbc = CF δac , CF = = a c 2Nc 3 P AB ACD BCD AB C,D f f = CAδ , CA = Nc = 3 P b a 1 −1 A A 1 − 1 = tabtcd = δbc δad δabδcd (Fierz) 2 2N 2 2Nc c d The QCD coupling is running Quantum corrections alter particle masses and couplings Ultraviolet divergences removed by renormalisation Renormalisation intro duces a mass scale the subtraction coupling p oint of UV divergences and the renormalised s dep ends on s s ln N n of active avours N n C f C f MeV is an integration constant QCD d s s s d Asymptotic freedom as s we can use p erturbation theory for pro cesses involving large momentum scales small distances is crucial in QED and increases as Sign of Infrared slavery as s connement quarks gluons are only found in coloursinglet b ound states we have to use nonp erturbative metho ds eg lattice at low momentum scales large distances Running of has b een established exp erimentally s 0.5 Theory Data NLO NNLO αs(Q) Lattice Deep Inelastic Scattering e+e- Annihilation 0.4 Hadron Collisions Heavy Quarkonia Λ(5) MS α s (Μ Z ) 251 MeV 0.1215 0.3 QCD 4 213 MeV 0.1184 O(α s ) { 178 MeV 0.1153 0.2 0.1 1 10 100 Q [GeV] Compilation of data by Siggi Bethke Measurements