Jefferson Lab/Hampton U Lepton Scattering as a Probe of Hadronic Structure Andrei Afanasev Jefferson Lab/Hampton U USA HEP School, January 11-13, 2010, Valparaiso, Chile

Plan of Lectures Introduction to particle scattering formalism Basics Scattering cross section, spin asymmetries Experimental data on nucleon form factors Derivation of basic formulae Overview of lepton scattering processes, experimental results and future programs

Some Facts about Quarks, Hadrons and Nuclei

Some facts (cont.)

Elementary Particles

Hadrons and Interactions Quarks carry both electromagnetic charge and color charge

Scattering as a Probe of Structure Rutherford experiment (1909-1911) Beam: alpha-particles from radioactive 214Po Target: gold foil Result: “Planetary Model” of an atom; beginning of a new era in modern physics Compare with a bullet probing a haystack Exercise: Run a computer simulation of Rutherford experiment http://phet.colorado.edu/simulations/sims.php?sim=Rutherford_Scattering

Scattering in Quantum Physics Described by a Lippmann-Schwinger equation for wave function of the scattered particles, Differential cross section:

Born Approximation Scattering amplitude and differential cross section in the first Born approximation

Role of Particle Spin Spin is an internal quantum number of a particle For charged particles spin relates to their magnetic moments through a Bohr magneton Spin has discrete projection on a selected direction (quantum phenomenon), demonstrated in Stern-Gerlach experiment (1922) for a beam of spin-1/2 particles Exercise: run a computer simulation of a Stern-Gerlach experiment at http://phet.colorado.edu/simulations/sims.php?sim=SternGerlach_Experiment

Electron Scattering

Pros and Cons of Electron Scattering

Elastic Electron Scattering Form Factor response of system to momentum transfer Q, often normalized to that of point-like system Examples: scattering of photons by bound atoms nuclear beta decay X-ray scattering from crystal electron scattering off nucleon

Form Factors F(q2)=1/(1+q2/μ2)2 Exercise: Calculate the charge distribution ρ(x) is the form factor is described by a dipole formula F(q2)=1/(1+q2/μ2)2

Nucleon Electro-Magnetic Form Factors Fundamental ingredients in “Classical” nuclear theory A testing ground for theories constructing nucleons from quarks and gluons - spatial distribution of charge, magnetization wavelength of probe can be tuned by selecting momentum transfer Q: < 0.1 GeV2 integral quantities (charge radius,…) 0.1-10 GeV2 internal structure of nucleon > 20 GeV2 pQCD scaling Caveat: If Q is several times the nucleon mass (~Compton wavelength), dynamical effects due to relativistic boosts are introduced, making physical interpretation more difficult Additional insights can be gained from the measurement of the form factors of nucleons embedded in the nuclear medium - implications for binding, equation of state, EMC… - precursor to QGP

Formalism Sachs Charge and Magnetization Form Factors GE and GM with E (E’) incoming (outgoing) energy, q scattering angle, k anomalous magnetic moment In the Breit (centre-of-mass) frame the Sachs FF can be written as the Fourier transforms of the charge and magnetization radial density distributions GE and GM are often alternatively expressed in the Dirac (non-spin-flip) F1 and Pauli (spin-flip) F2 Form Factors

Elastic Nucleon Form Factors Based on one-photon exchange approximation Two techniques to measure Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross

Do the techniques agree? SLAC/Rosenbluth ~5% difference in cross-section x5 difference in polarization JLab/Polarization Both early SLAC and Recent JLab experiments on (super)Rosenbluth separations followed Ge/Gm~const JLab measurements using polarization transfer technique give different results (Jones’00, Gayou’02) Radiative corrections, in particular, a short-range part of 2-photon exchange is a likely origin of the discrepancy

Basics of QED radiative corrections (First) Born approximation Initial-state radiation Final-state radiation Cross section ~ dω/ω => integral diverges logarithmically: IR catastrophe Vertex correction => cancels divergent terms; Schwinger (1949) Multiple soft-photon emission: solved by exponentiation, Yennie-Frautschi-Suura (YFS), 1961

Complete radiative correction in O(αem ) Radiative Corrections: Electron vertex correction (a) Vacuum polarization (b) Electron bremsstrahlung (c,d) Two-photon exchange (e,f) Proton vertex and VCS (g,h) Corrections (e-h) depend on the nucleon structure Meister&Yennie; Mo&Tsai Further work by Bardin&Shumeiko; Maximon&Tjon; AA, Akushevich, Merenkov; Guichon&Vanderhaeghen’03: Can (e-f) account for the Rosenbluth vs. polarization experimental discrepancy? Look for ~3% ... Log-enhanced but calculable (a,c,d) Main issue: Corrections dependent on nucleon structure Model calculations: Blunden, Melnitchouk,Tjon, Phys.Rev.Lett.91:142304,2003 Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004