1. Radiative Corrections for Pion Electro-production Including Two-Photon Exchange
Andrei Afanasev
The George Washington University, Washington, DC
Radiative Corrections in Annihilation and Scattering Experiments
Orsay, Oct 7-8, 2013

2. Plan of talk Radiative corrections for charged lepton scattering
Model-independent and model-dependent; soft and hard photons
Refined bremsstrahlung calculations
Muon vs electron scattering
Two-photon exchange for electroproduction of pions

3. Critical Role of Rad.Corrections: Elastic ep-scattering
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

4. Complete radiative correction in O(αQED)
Radiative Corrections:
Electron vertex correction (a)
Vacuum polarization (b)
Electron bremsstrahlung (c,d)
Two-photon exchange (e,f)
Proton vertex and Virtual Compton (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 “model-independent”(a,c,d)
Two-photon Corrections dependent on nucleon structure
Model calculations:
Blunden, Melnitchouk,Tjon, Phys.Rev.Lett.91:142304,2003; Phys.Rev.C72:034612,2005
AA, Brodsky, Carlson, Vanderhaeghen, Chen, PRL 93:122301,2004; PRD72:013008,2005

5. Logarithmic Enhancement
An electron is lighter than a muon, radiates easier
Compare lepton mass-dependent terms in Schwinger correction:
Bremsstrahlung is suppressed logarithmically for muons (~factor 3-4)
Two-photon exchange effects same for electrons and muons (for El>>ml)
For low Q2<<ml2, the correction is of the order

6. Basic Approaches to QED Corrections
L.W. Mo, Y.S. Tsai, Rev. Mod. Phys. 41, 205 (1969); Y.S. Tsai, Preprint SLAC-PUB-848 (1971).
Considered both elastic and inelastic inclusive cases. No polarization.
D.Yu. Bardin, N.M. Shumeiko, Nucl. Phys. B127, 242 (1977).
Covariant approach to the IR problem. Later extended to inclusive, semi-exclusive and exclusive reactions with polarization.
RADGEN: Monte Carlo of p(e,e’)X including radiative events
E.A. Kuraev, V.S. Fadin, Yad.Fiz. 41, 7333 (1985); E.A. Kuraev, N.P.Merenkov, V.S. Fadin, Yad. Fiz. 47, 1593 (1988).
Developed a method of electron structure functions based on Drell-Yan representation; currently widely used at e+e- colliders.

7. Electron Structure Functions (Kuraev,Fadin,Merenkov)
For polarized ep->e’X scattering, AA et al, JETP 98, 403 (2004); elastic ep: AA et al. PRD 64, (2001).
Resummation technique for collinear photons (=peaking approx.)
Resummed are large-log terms ln(Q2/ml2)
ln(Q2/ml2)~15(electron),~6(muon) at Q2~1GeV2
For elastic ep the difference <0.5% from previous calculation including hard brem

8. Electron Structure Functions for DIS
For polarized ep scattering, AA et al, JETP 98, 403 (2004)
Resummation technique
xB= 0.5; V= 10 GeV2

9. Separating soft 2-photon exchange
Tsai; Maximon & Tjon (k→0); similar to Coulomb corrections at low Q2
Grammer &Yennie prescription PRD 8, 4332 (1973) (also applied in QCD calculations)
Shown is the resulting (soft) QED correction to cross section
Already included in experimental data analysis
NB: Corresponding effect to polarization transfer and/or asymmetry is zero
Correction is independent of lepton mass: same for electrons or muons ε
q1→q
q2→0
Q2= 6 GeV2
δSoft
A similar approach can be applied for any exclusive reaction
Semi-inclusive? Problem: soft photons do not resolve short scales

10. Exchange of two hard photons
2-photon exchange contributions for non-soft intermediate photons
Can estimate based on a text-book example from Berestetsky, Lifshitz, Pitaevsky: Quantum Electrodynamics - originally due to Gorshkov, Gribov, Lipatov, Frolov (1967)
Double-log asymptotics of electron-quark backward scattering
Negative sign for backward ep-scattering; zero for forward scattering → Can (at least partially) mimic the electric form factor contribution to the Rosenbluth cross section
Numerically ~3-4% (for SLAC kinematics and mq~300 MeV)
Motivates a more detailed calculation of 2-photon exchange at quark level

11. Calculations using Generalized Parton Distributions
Model schematics:
Hard eq-interaction
GPDs describe quark emission/absorption
Soft/hard separation
Use Grammer-Yennie prescription
Soft photons are long-wavelength, do not resolve quarks
Hard photons interact with quarks (GPD model)
AA, Brodsky, Carlson, Chen, Vanderhaeghen,
Phys.Rev.Lett.93:122301,2004; Phys.Rev.D72:013008,2005

12. Updated Ge/Gm plot AA, Brodsky, Carlson, Chen, Vanderhaeghen,
Phys.Rev.Lett.93:122301, 2004; Phys.Rev.D72:013008, 2005

13. Full Calculation of Bethe-Heitler Contribution
Additional work by AA et al., using MASCARAD (Phys.Rev.D64:113009,2001)
Full calculation including soft and hard bremsstrahlung
Radiative leptonic tensor in full form
AA et al, PLB 514, 269 (2001)
Additional effect of full soft+hard brem → +1.2% correction to ε-slope

14. RC for Exclusive Electroproduction of Pions
AA, Akushevich, Burkert, Joo, Phys.Rev.D66, (2002)
Conventional RC, precise treatment of phase space, no peaking approximation, no dependence on hard/soft photon separation; extension to DVMP is straightforward
Can be used for any exclusive electroproduction of 2 hadrons, e.g., d(e,e’p)n (EXCLURAD code)
More appropriate for Deep-Virtual Meson Production with muons (compared to peaking-approximation-based approaches)
Used in data analysis at Jlab (and MIT, HERMES, MAMI,…)

15. Radiative Corrections for Exclusive Processes
Photon emission is a part of any electron scattering process: accelerated charges radiate
Exclusive electron scattering processes such as p(e,e’h1)h2 are in fact inclusive p(e,e’h1)h2 nγ ,
where we can produce an infinite number of low-energy photons
But low-energy photons do not affect polarization observables, thanks to Low theorem

16. Exclurad updated to include polarization (work with K. Joo)
Corrections to single-spin beam and target asymmetries and double-spin beam-target asymmetry
Target polarized along the beam direction

17. RC for target single-spin asymmetry

18. RC for beam-target asymmetry

19. Angular Dependence of Rad.Corrections
Rad.Corrections introduce additional angular dependence on the experimentally observed cross section of electroproduction processes, both exclusive and semi-inclusive

20. Two-Photon Exchange in Exclusive Electroproduction of Pions (same for muons!)
Standard contributions: EXCLURAD
Additional contributions due to two-photon exchange, calculated by AA, Aleksejevs, Barkanova, arXiv: (Phys.Rev. D88 (2013) ) Calculated in soft-photon approximation
1+δ ε
Calculated ε-dependence of TPE correction.
Q2=6 GeV2, W=3.2 GeV, Ee=5.5 GeV .
Shows ±2% variation with ε.

21. TPE in Delta-resonance region (angular dependence)

22. TPE in Delta-resonance region (epsilon-dependence)

23. TPE for deep-virtual kinematics

24. PE for pion form factor measurement kinematics (JLAB Experiment 12-06-01, Huber et al)

25. Angular dependence of “soft” corrections arXiv:1207.1767

26. Soft photon corrections vs kinematics arXiv:1207.1767

27. Results for Exclusive Pion Production Phys. Rev
Results for Exclusive Pion Production Phys.Rev. D88 (2013) (arXiv: )
Soft photon exchange
Dependence on IR photon separation
Obtained model-independent corrections, applicable to SIDIS
Soft-photon contributions expressed in terms of Passarino-Veltman integrals
Can be added to existing codes and/or generators and studied for specific experimental conditions
Equally applicable to muon scattering (important for DVMP at COMPASS)

28. Two-Photon Exchange in inclusive DIS
Theory: Afanasev, Strikman, Weiss, Phys.Rev.D77:014028,2008
Asymmetry due to 2γ-exchange ~1/137 suppression
Addional suppression due to transversity parton density => predict asymmetry at ~10-4 level
EM gauge invariance is crucial for cancellation of
collinear divergence in theory predictions
Prediction consistent with HERMES measurements who set upper limits ~( )x10-3 : Phys.Lett.B682: ,2010