1. How to probe the quarks? Scatter high-energy electron off a proton: Deep-Inelastic Scattering (DIS) Highest energy e-p collider: HERA at DESY in Hamburg: ~ 300 GeV Relevant scales:

Deep-Inelastic Electron Scattering DIS kinematics: Four-momentum transfer: Mott Cross Section (  c=1 ): Electron scattering of a spinless point particle

Effect of proton spin: –Mott cross section: –Effect proton spin  helicity conservation 0 deg.:  ep (magnetic)  deg.: spin-flip!  magn ~  Ruth sin 2 (  /2) ~  Mott tan 2 (  /2) with Nucleon form factors: with: The size of the nucleon: –proton: r p = 0.86 fm –neutron: r n = 0.10 fm Electron-proton scattering Mass of target = proton

Hofstadter, R., et al., Phys. Rev. 92, 978 (1953)

Excited states of the nucleon Scatter 4.9 GeV electrons from a hydrogen target: Why use invariant energy? Evaluate invariant energy of virtual-photon proton system: In the lab-frame: P = (m p,0)  → What do we see in the data for W > 2 GeV ?  (1232) Observation excited states : Nucleons are composite

Looking deep inside the proton First SLAC experiment (‘69): –expected from proton form factor: First data show big surprise: –very weak Q 2 -dependence : –scattering off point-like objects? How to proceed : –Find more suitable variable –What is the meaning of or the ‘effective form factor’? As often at such a moment…. …. introduce a clever model!

Stanford Linear Accelerator Center

Look familiar…?..... HMS in Hall C

The Quark-Parton Model Assumptions: –Neglect masses and p T ’ ’s –Proton constituent = Parton –Impulse Approximation: Lets assume: p quark = xP proton –Since xP 2  M 2 <<Q 2 it follows: e P parton e’ Quasi-elastic scattering off partons Check limiting case: Therefore: x = 1: elastic scattering and 0 < x < 1 Definition Bjorken scaling variable

Cross section for deep-inelastic scattering Cross section: with –Mott cross section : scattering off point charge –Structure functions W 1, W 2 with dimension [GeV] -1 –Key issue: if quark is not a fermion we will find W 1 =0 Inelastic Electron Scattering electron quark

Structure Functions F 1, F 2 homework Introduce dimensionless structure functions: Rewrite this in terms of : (elastic e-q scatt.: 2m q = Q 2 ) Experimental data for 2xF 1 (x) / F 2 (x) → quarks have spin 1/2 (if bosons: no spin-flip  F 1 (x) = 0) Solution

Interpretation of F 1 (x) and F 2 (x) Distinguish –Valence quarks (N-prop.) –Sea quarks –derived from: In the quark-parton model: [and F 2 = 2xF 1 analogously] Quark momentum distribution Heisenberg requires: –Gluon emission: presence of virtual -pairs

The quark structure of nucleons Quark quantum numbers: –Spin: ½  S p,n = (  ) = ½ –Isopin: ½  I p,n = (  ) = ½ Why fractional charges? –Extreme baryons: Z = –Assign: z up =+ 2/3, z down = - 1/3 Three families: –m c,b,t >> m u,d,s : no role in p,n Structure functions: –Isospin symmetry: –‘Average’ nucleon F 2 (x) with q(x) = q v (x) + q s (x) etc. Neutrinos:

Neglect strange quarks  –Data confirm factor 5/18: Evidence for fractional charges Fraction of proton momentum carried by quarks: –50% of momentum due to non- electro-weak particles: Evidence for gluons Fractional quark charges

Quarks in protons & neutrons If q s p (x) = q s n (x) and x  0 : In the limit x  1: –assume same high- x tail: –assume instead isospin symmetry: Extract F 2 n / F 2 p from data: → u -quark dominance

Modern data First data (1980): “Scaling violations”: –weak Q 2 dependence –rise at low x –what physics?? PDG 2002 ….. QCD

g Quantum Chromodynamics (QCD) Field theory for strong interaction: –quarks interact by gluon exchange –quarks carry a ‘colour’ charge –exchange bosons (gluons) carry colour  self-interactions (cf. QED!) Hadrons are colour neutral: –RR, BB, GG or RGB –leads to confinement: Effective strength ~ #gluons exch. –low Q 2 : more g’s: large eff. coupling –high Q 2 : few g’s: small eff. coupling q q q q g

The QCD Lagrangian (j,k = 1,2,3 refer to colour; q = u,d,s refers to flavour; a = 1,..,8 to gluon fields) Covariant derivative: Gluon kinetic energy term Gluon self- interaction Free quarks qg-interactions SU(3) generators:

PDG 2002 QCD predictions: the running of  s pQCD valid if  s << 1 :  Q 2 > 1.0 (GeV/c) 2 pQCD calculation: –with  exp = 250 MeV/c:  asymptotic freedom  confinement Running coupling constant is best quantitative test of QCD. CERN 2004

QCD predictions: scaling violations Originally: F 2 = F 2 (x) –but also Q 2 - dependence Why scaling violations? –if Q 2 increases:  more resolution ( ~1/ Q 2 )  more sea quarks +gluons QCD improved QPM: Officially known as: Altarelli-Parisi Equations (“DGLAP”)

QCD fits of F 2 (x,Q 2 ) data Free parameters: –coupling constant: –quark distribution q(x,Q 2 ) –gluon distribution g(x,Q 2 ) Successful fit: Corner stone of QCD Nucleon structure: Unique self-replicating structure Quarks Gluons

Summary of key QCD successes The ‘converted’ distance dependence of  s : The data on the structure function F 2 (x,Q 2 ):

The problem of QCD If  s >1 perturbative expansions fail… Extrapolate  s to the size of the proton, m:  Non-perturbative QCD: – Proton structure & spin – Confinement – Nucleon-Nucleon forces – Higher twist….. Lattice QCD simulations…

Summary Quarks are the constituents of the proton Quark carry only 50% of the proton momentum QCD describes quark-gluon interactions: –Successful description scaling violations –Running coupling constant –But non-pQCD is insufficient at r ~ r proton What JLab (and others) are looking into: –Non-pQCD effects –The origin of the spin of the proton –The role of gluons and orbital angular momentum –Generalized parton distributions –Transversity