BRIEF INTRODUCTION TO HERA PHYSICS aim: get to exercises as soon as possible cover: HERA accelarator and experiments DIS kinematics, how to compare theory and data:mc generators ==> next step: use them! many topics not covered, questions left open: please ask, we can discuss them e.g. next week! relativistic kinematic and 4 vectors (will be covered by exercises, if you would like a reminder : please ask!) history of ep physics and bigger picture details of (most) important part of HERA physics: structure of the proton and parton evolution surprises and important results from HERA details on how MC generators work these topics we can discuss next week and/or will be covered by summerstudent lectures (H. Jung, J. Meyer, T. Haas)
SCATTERING EXPERIMENTS - HISTORY 1911 Rutherford gold foil experiment angular distribution (large scattering angles) ==> atomic nucleus 1950s Hofstadter, McAllister electron scattering in atomic nuclei ==> nucleon: n,p 1968 Stanford Linear Accelerator Center (SLAC) first: electron scattering of quarks in the proton point like spin1/ constituents of the nucleon nucleus nucleon partons important for development of Quark-Parton-Model and QCD! since 199 HERA first (and only) ep collider highest momentum transfer Q s 100000 GeV highest resolution ~ 10-3 fm (SLAC: 1/30 fm) resolve the structure of the proton...
HERA
HERA
DIS KINEMATICS,k Kinematics: Lorentz-Invariants: center of mass energy s s = (e + p) ¼ 90000GeV photon 4-vector q q = pe p0e virtual photon q negative 4-momentum transfer squared Q Q = q = (pe p0e ) Invariant mass of hadronic final state W W = ( + p) interpretation of Q : resolution power
DIS KINEMATICS,k Kinematics: Lorentz-Invariants: bjorken variables p q y p k Q Scaling variable x p q Inelasticiy y useful relations: s= mp Q Q + ¼ xy xy! Q = (s m )xy ¼ xys
DIS KINEMATICS,k Kinematics: Lorentz-Invariants: bjorken variables p q y p k Q Scaling variable x p q Inelasticiy y interpretation of y: in the proton rest frame: E y= Ee = fractional photon energy, lorentz invariance???
DIS KINEMATICS,k Kinematics: Lorentz-Invariants: p' zp * Infinite momentum frame: proton faaaaaaaaaaast no interaction between partons (incoherent scattering of one parton) as in QPM neglect partons and proton mass Q x p q interpretation of x: in the infinite momentum frame * z = momentum fraction of struck parton parton momentum (i.s.) = zp parton momentum (f.s.) = p' Q 0 (zp + q) = p x p q! z = x + ::: ¼ x x can be interpreted as fraction of proton momentum carried by parton (only in the QPM or i.m.f.!)
DIS KINEMATICS exercises: calculate s @ HERA calculate E of e beam for a fixed target experiment with same s p q y p k Q = q = (k k 0 ) Q x p q calculate Q and y from the scattered electron (Ee,Ee', (choose... in which frame?) calculate relation between x and z what is Q and xmin at a fixed max target experiment (Ep=0) 0 1 0 E0 Ee 0 B C B 0 E sin µ C B k0 = B k = @ A @ 0 0 E 0 cos µ Ee 1 Ep B C C C p=b 0 C @ 0 A A Ep 1 polar angle w.r.t. proton beam direction=positive z-axis 0
KINEMATIC PLANE
Quantum Chromo Dynamics quantum field theory of strong force QCD analogy in QED: color charge quarks in three different colors: red, green, blue electric charge symmetry group SU(3)c U(1) em gauge bosons: gluons gluons carry color (color & anticolor) vertices: quark-antiquark pairproduction / annihilation or radiation/absorption of a gluon gluon self interactions: gauge boson: electrically neutral vertices: e+e- pairproduction / annihilation or radiation/absorption of a photon
QCD: running coupling confinement and asymptotic freedom QCD: consequence of gluon selfinteraction: running coupling S(Q) Q momentum transfer increasing distance x * ==> decreasing Q ==> increasing S confinement antiscreening of electric charge: quark-antiquark pairs: screening gg pairs: antiscreening decreasing distance x ==> increasing Q ==> decreasing S asymptotic freedom QED: ~1/137 em Running coupling em(q) Q momentum transfer increasing distance x * ==> decreasing Q ==> decreasing em screening of electric charge: +- pairs: screening Q x >» ~ Learn more: next week in lecture ontheory of Elementary Particles!!!
QCD: running coupling 4¼ s (Q ) = (11 =3nf ) log (Q = QCD ) perturbation theory in orders of s only possible at high Q at low Q s gets large and perturbation series does not converge
DIS @ HERA higher orders of QCD 0s lowest order QCD calculations in perturbative QCD available up to Approximate higher orders... 3s
DIS @ HERA higher orders of QCD Approximate higher orders...... by Partonshowers = succesive gluon radiations ==> parton cascades in initial or final state parton evolution described by different approximations initial state: what happens inside the proton? non-pert. Process absorbed in parton density functions pert. part : parton showers final state: splitting into many partons: scale & s % non perturbative process: haronisation no calculation possible, need models! detector: only color neutral hadrons no quarks or gluons!
DIS @ HERA higher orders of QCD Approximate higher orders...... by Partonshowers = succesive gluon radiations ==> parton cascades in initial or final state parton evolution described by different approximations detector: only color neutral hadrons no quarks or gluons! initial state: what happens inside the proton? non-pert. Process absorbed in parton density functions pert. part : parton showers final state: splitting into many partons: scale & s % non perturbative process: haronisation no calculation possible, need models! learn more about parton evolution, proton structure and pdfs later
MC GENERATORS THEORY QED QCD pert. calculations e.g. Matrixelement --> ¾ q approximation/models for higher order effects e.g. Parton shower, Parton evolution Non-perturbative effects: Inside the proton: parton density functions final state: hadronisation models How to compare data and theory? Combine different models and ansaetze in MC event generators MC used for Correcting data Comparison with data Prestudies for new analyses MC EVENT GENERATOR kind of process genereated Q,x,y DETECTOR list of hadrons list of partons initial state MC EVENT *more details on MC generators next week (Tobias and Hannes) Signal in subdetectors RECONSTRUCTED DATA tracks (track detectors) cluster (calo) ==> jets and particles reconstructed Q,x,y correction: MC events + detecor simul. CORRECTED DATA (corrected for det effects)
MC GENERATORS & HZTOOL HZTOOL RAPGAP fortran package get final state from MC generator loop over generated final state objects PYTHIA MC GENERATORS (many different * learn more next week!) can included data histos same subroutine can be used with different MC generators many tools available CASCADE DJANGO HERWIG... do your analysis DATA
DIS KINEMATICS,k Kinematics: Lorentz-Invariants: center of mass energy s s = (e + p) 4-momentum transfer squared Q Q = q = (pe p0e ) Invariant mass of hadronic final state W W = ( + p) Bjorken x and y Deep : Q large Inelastic: proton breaks up, W large Q x p q p q y p k
ELECTRON SCATTERING Scattering of electrons on pointlike particles: Mott cross section d¾ d¾ d¾ d¾ µ = = F (q ) = F (q ) cos d d d MOTT d RUTH RUTH 4E sin4 µ= Formfactor Rutherford e spin 1/ Scattering on pointlike spin ½ particles: µ d¾ d¾ µ q µ = cos sin d d RUTH m Additional term : target with spin 1/ Inelastic ep scattering: µ d¾ d¾ µ µ = W (º; Q )cos + W1 (º; Q )sin d d RUTH µ d¾ d¾ µ µ = = W (º; Q )cos + W1 (º; Q )tan d d MOTT Q x= mº ³ q p º= M Bjorken scaling scattering on pointlike spin 1/ consituents in the proton --> at high Q : elastic scattering of quarks --> W1, W functions of Q ==> scaling =º (= x) m
DISCOVERY OF PROTON SUBSTRUCTURE Compare cross sectinon with Mott cross section: F = ºW only small dependence on Q interpretation by R. Feynman: F= W momentum distribution of partons ==> Quark Parton model Elastic scattering: proton stays intact: W=M, x=1, described by Q inelastic scattering: W > M -> additional variable x cross section / Mott cross section - almost constant with Q W = (q + P ) = q + M + q P x = Q =P q 1 W = M + Q ( 1) x
DISCOVERY OF PROTON SUBSTRUCTURE Plot proposed by Bjorken: F= W as function of Q
DEEP INELASTIC ep SCATTERING - QPM electron radiates photon known from QED Leptonic tensor Unknown what happens inside the proton? QCD? Hadronic tensor d¾» leptonic tensor hadronic tensor
PROTON STRUCTURE 1 quark proton=pointlike particle, no structure 3 quarks each quark carries 1/3 of proton momentum x=1/3 3 bound valence quarks enter: the gluon 3 quarks share proton momentum 3 bound valence quarks and sea quarks valence and seaquarks (and gluons) share proton momntum very low momentum fractions possible qq sea!