1. Andrei Afanasev, Trento, 6/13/07 Higher-Order Electromagnetic Corrections in SIDIS Andrei Afanasev Hampton University/Jefferson Lab Talk Presented at ECT Workshop Transverse momentum, spin, and position distributions of partons in hadrons

2. Andrei Afanasev, Trento, 6/13/07 Plan of Talk. QED radiative corrections overview. Bremsstrahlung corrections for SIDIS. Cross section. Moments. SSA from two-photon exchange in inclusive DIS. Role of transversity. Interplay of non-partonic and partonic mechanisms for two-photon exchange; Cancellation of divergences. Outlook

3. Andrei Afanasev, Trento, 6/13/07 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

4. Andrei Afanasev, Trento, 6/13/07 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.. 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.

5. Andrei Afanasev, Trento, 6/13/07 Electron Structure Functions. For polarized ep scattering, AA et al, JETP 98, 403 (2004). Resummation technique x B = 0.5; V= 10 GeV 2

6. Andrei Afanasev, Trento, 6/13/07 RC for 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 (EXCLURAD code). Can be used for any exclusive electroproduction of 2 hadrons, e.g., d(e,ep)n See http://www.jlab.org/RC for other codeshttp://www.jlab.org/RC Used in data analysis at JLab (and MIT, HERMES, MAMI,…)

7. Andrei Afanasev, Trento, 6/13/07 HAPRAD. Fortran code for rad.corrections in SIDIS. O(α) correction. Uses Bardin-Shumeiko covariant technique for IR cancellation. Available from www.jlab.org/RCwww.jlab.org/RC. See description in I. Akushevich et al, Eur.Phys.J.C10:681-687, 1999.

8. Andrei Afanasev, Trento, 6/13/07 HAPRAD results [Akushevich et al.99] δ=σ obs /σ Born

9. Andrei Afanasev, Trento, 6/13/07 Azimuthal angular dependence of rad.correction. Rad.correction is a function of kinematic invariants k 1 ·p h, k 2 ·p h, …,. Which are functions of cos(φ) leading to nonzero cos(φ), cos(2φ), cos(3φ),… moments. Sin(nφ) dependence does not appear (for unpolarized particles) due to parity

10. Andrei Afanasev, Trento, 6/13/07 moment from photon radiation. Assume =0 for Born cross section x B =0.2x B =0.3 z=0.600.18E-2 z=0.70.12E-20.35E-2 z=0.80.08E-20.22E-2 for E=5.7 GeV, p T =0.4 GeV,Q 2 =2 GeV 2

11. Andrei Afanasev, Trento, 6/13/07 Rad.correction to Cahn effect JLAB kinematics obs / Born for E=5.7 GeV, p T =0.4 GeV,Q 2 =2 GeV 2 x B =0.2x B =0.3 z=0.60.91 z=0.70.920.96 z=0.80.940.98

12. Andrei Afanasev, Trento, 6/13/07 Summary on brem correction. Rad.correction for Cahn effect evaluated at 10% level. Correction depends on a model used for pT-dependence. Generate =0.001-0.002. Conclude: Iteration procedure required for data analysis. Further improvements:. Radiative tail from exclusive process N(e,eπ)N. Contribution of nucleon resonance region

13. Andrei Afanasev, Trento, 6/13/07 Single-Spin Asymmetries in DIS from 2-photon exchange AA, M. Strikman, and C.Weiss

14. Andrei Afanasev, Trento, 6/13/07 Motivation. Motivated by experimental+theoretical two-photon exchange studies at JLab. Implications for SIDIS: Measured SSA in (e,eh) are of the order of a few per cent. What if higher-order electromagnetic correction is also a few per cent? => Then EM-generated SSA would become a major problem. Recent calculation of normal target asymmetry from two-photon exchange in a parton model obtained a divergent result, see. A. Metz, M. Schlegel, K. Goeke Phys.Lett.B643:319-324,2006; e-Print Archive: hep-ph/0610112

15. Andrei Afanasev, Trento, 6/13/07 Transverse target spin dependence in eNeX

16. Andrei Afanasev, Trento, 6/13/07 Spin dependence with two-photon exchange

17. Andrei Afanasev, Trento, 6/13/07 Example: Point-like spin-1/2 target Barut, Fronsdal, 1960;…

18. Andrei Afanasev, Trento, 6/13/07 Composite nucleon approximation Within reach of experiment polarized He3 X.Jiang et al JLAB PR-07-013

19. Andrei Afanasev, Trento, 6/13/07 Divergence cancellation. Divergence: terms of the type ln(Q 2 /λ 2 ), where λ is a cut-off parameter (`photon mass); final results should be independent of λ. Two kinds of divergence appear at intermediate steps:. Infra-red: exchanged photon momentum 0. Such divergent terms result in a spin-independent common factor appearing in front of one-photon exchange amplitude; the factors cancel in the result for asymmetry (difference σ n+ -σ n- ). Collinear: intermediate photon is collinear to the parent electron, while carrying substantial energy: Divergence cancels at the amplitude level; electromagnetic current conservation for the Compton tensor is essential (see AA,Merenkov04 proof for elastic ep-scattering)

20. Andrei Afanasev, Trento, 6/13/07 Normal Asymmetry: Elastic epep (AA, Merenkov) EM gauge invariance important for cancellation of collinear singularity for unpolarized beam Feature of the normal beam asymmetry: After m e is factored out, the remaining expression is singular when virtuality of the photons reach zero in the loop integral. Also calculations by Vanderhaeghen, Pasquini (2004); Gorchtein (2005); Borisyuk&Kobushkin (2005) confirm quasi-real photon exchange enhancement of inelastic intermediate excitations

21. Andrei Afanasev, Trento, 6/13/07 Model example. Collinear divergence ~ln(Q 2 /λ 2 ) from diagram (a) precisely cancels the divergence of the diagram (b). Divergence disappeared before integration over p 2 => no enhancement of the effect in SIDIS and inclusive. To obtain sensible results for the single-spin asymmetry from two-photon exchange, need to work with models that exactly satisfy electromagnetic current conservation for the (inelastic) virtual Compton amplitude

22. Andrei Afanasev, Trento, 6/13/07 Summary. Bremsstahlung rad.correction to SIDIS cross section is tens of per cent. Azimuthal dependence of rad.corrections not negligible, leading to10% (relative) correction to Cahn asymmetry, and (absolute) 0.001÷0.002. Model dependence Iteration procedure necessary for data analysis. Target SSA from two-photon exchange in DIS estimated in a model at 10 -4. Neglecting electromagnetic current conservation results in (unphysical) collinear divergence in SSA induced by two-photon exchange; divergence absent for gauge-invariant Compton tensor. Expect log-enhanced ~log(Q 2 /m e 2 ) higher-twist effects for beam SSA (measurable in parity-violating DIS setup at JLab)

23. Andrei Afanasev, Trento, 6/13/07 Remember of radiation safety!