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

2. 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

3. Some Facts about Quarks, Hadrons and Nuclei

4. Some facts (cont.)

5. Elementary Particles

6. Hadrons and Interactions
Quarks carry both electromagnetic charge and color charge

7. Scattering as a Probe of Structure
Rutherford experiment ( )
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

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

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

10. 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

11. Electron Scattering

12. Pros and Cons of Electron Scattering

13. 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

14. 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

15. 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,…)
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

16. 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

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

18. 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

19. 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

20. 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