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

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

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

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

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

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.

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, 113009 (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

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

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

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

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

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

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

RC for Exclusive Electroproduction of Pions AA, Akushevich, Burkert, Joo, Phys.Rev.D66, 074004 (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,…)

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

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

RC for target single-spin asymmetry

RC for beam-target asymmetry

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

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:1207.1767 (Phys.Rev. D88 (2013) 053008) 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.

TPE in Delta-resonance region (angular dependence)

TPE in Delta-resonance region (epsilon-dependence)

TPE for deep-virtual kinematics

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

Angular dependence of “soft” corrections arXiv:1207.1767

Soft photon corrections vs kinematics arXiv:1207.1767

Results for Exclusive Pion Production Phys. Rev Results for Exclusive Pion Production Phys.Rev. D88 (2013) 053008 (arXiv:1207.1767) 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)

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 ~(0.6-0.9)x10-3 : Phys.Lett.B682:351-354,2010