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Radiative Corrections for Pion Electro-production Including Two-Photon Exchange

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.

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Radiative Corrections for Pion Electro-production Including Two-Photon Exchange

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  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 • 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 SLAC/Rosenbluth ~5% difference in cross-section x5 difference in polarization JLab/Polarization

  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, 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

  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= 6 GeV2 q2→0 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, 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,…)

  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: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.

  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” correctionsarXiv:1207.1767

  26. Soft photon corrections vs kinematicsarXiv:1207.1767

  27. Results for Exclusive Pion ProductionPhys.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)

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

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