1. Two-photon physics in hadronic processes Marc Vanderhaeghen College of William & Mary / Jefferson Lab PPP7 workshop, Taipei, June 7 - 10, 2007

2. Outline Elastic eN scattering beyond the one-photon exchange approximation puzzle of different results extracted for G E /G M in Rosenbluth vs polarization experiments two-photon exchange processes Beam (target) normal spin asymmetry in elastic eN scattering new observable : absorptive part of double Virtual Compton Scattering (VCS) amplitude resonance region, diffractive region, partonic estimate (GPDs) in coll. with A.Afanasev, S. Brodsky, C. Carlson, Y.C. Chen, M. Gorchtein, P.A.M. Guichon, V. Pascalutsa, B. Pasquini Carlson, Vdh : Ann. Rev. Nucl. Part. Sci. 57 (2007) 171-204

3. Early Measurements of G E p relied on Rosenbluth separation measure d  /d  at constant Q 2 G E p inversely weighted with Q 2, increasing the systematic error above Q 2 ~ 1 GeV 2 At 6 GeV 2  R changes by only 8% from  =0 to  =1 if G E p =G M p /µ p Hence, measurement of G E p with 10% accuracy requires 1.6% cross-section measurement Method : at fixed Q2, vary angle  (or equivalently  ) and plot reduced cross section versus 

4. Spin Transfer Reaction 1 H(e,e’p) No error contributions from analyzing power beam polarimetry

5. Rosenbluth vs polarization transfer measurements of G E /G M of proton Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002) SLAC, Jlab Rosenbluth data Puzzle : two methods, two different results !

6. Speculation : missing radiative corrections Speculation : there are radiative corrections to Rosenbluth experiments that are important and are not included missing correction : linear in  not strongly Q 2 dependent G E term is proportionally smaller at large Q 2 if both FF scale in same way effect more visible at large Q 2 Q 2 = 6 GeV 2

7. Radiative correction diagrams bremsstrahlung vertex corrections 2 photon exchange box diagrams

8. Status of radiative corrections Tsai (1961), Mo & Tsai (1968) box diagram calculated using only nucleon intermediate state and using q 1 ¼ 0 or q 2 ¼ 0 in both numerator and denominator (calculate 3-point function) -> gives correct IR divergent terms Maximon & Tjon (2000) same as above, but make the above approximation only in numerator (calculate 4-point function) + use on-shell nucleon form factors in loop integral Blunden, Melnitchouk, Tjon (2003) further improvement by keeping the full numerator N

9. Elastic eN scattering beyond one-photon exchange approximation equivalently, introduce Kinematical invariants : (m e = 0)

10. Observables including two-photon exchange Real parts of two-photon amplitudes

11. Phenomenological analysis Guichon, Vdh (2003) 2-photon exchange corrections can become large on the Rosenbluth extraction,and are of different size for both observables relevance when extracting form factors at large Q 2

12. Two-photon exchange calculation : elastic contribution Blunden, Tjon, Melnitchouk (2003, 2005) N world Rosenbluth data Polarization Transfer

13. hard scattering amplitude electron helicityquark helicity Calculation for e  e  can be found in literature (e.g. van Nieuwenhuizen (1971) ), which we verified explicitly IR divergences of boxes must disappear or cancel in the end, regularize through photon mass Two-photon exchange : partonic calculation

14. kinematics partonic subprocess : Separation soft-hard parts in electron-quark box Follow the decomposition of Grammer and Yennie (1973) : soft part calculated as 3-point function reproduces Low Energy Theorem

15. hard scattering amplitude Two-photon exchange : partonic calculation GPD integrals “magnetic” GPD “electric” GPD “axial” GPD

16. Two-photon exchange : partonic calculation GPDs Chen, Afanasev, Brodsky, Carlson, Vdh (2004)

17. Experimental verification of TPE contributions Experimental verification (will be performed in next couple of years ! ) non-linearity in  -dependence (test of model calculations) transverse single-spin asymmetry (imaginary part of two-photon amplitude) ratio of e + p and e - p cross section (direct measurement of two-photon contributions) CLAS experiment E04-116 aims at a measurement of the  -dependence of the e + /e - ratio for Q 2 -values up to 2.0 GeV 2 At the VEPP-3 ring that ratio will be measured at two  and Q 2 -values

18. ε - dependence of TPE contributions (I) Chen, Kao, Yang (2007) Polynomial fit “log” fit 1γ only : Rosenbluth 1γ + 2γ : log fit 1γ + 2γ : polynomial fit

19. Q 2 (GeV 2 ) ε 010.20.40.60.8 1.75 3.25 5.00 e + p / e - p 1.00 1.10 1.12 ε 00.410.20.80.6 e + p / e - p 1.02 1.10 1.14 Chen, Kao, Yang (2007) polynomial fitlog fit ε - dependence of TPE contributions (II)

20. Polarization transfer observables  1  2  2  correction on is small 2  correction on can be tested at small 

21. proton Dirac & Pauli FFs : modified Regge GPD model PQCD Belitsky, Ji, Yuan (2003) GPD framework Guidal, Polyakov, Radyushkin, Vdh (2005) data : SLAC data : JLab/HallA

22. Normal spin asymmetries in elastic eN scattering on-shell intermediate state spin of beam OR target NORMAL to scattering plane directly proportional to the imaginary part of 2-photon exchange amplitudes OR order of magnitude estimates : target : beam :

23. time reversed states momenta and spins reversed rotation over 180 o around axis ? to plane phase SSA in elastic eN scattering

24. Unitarity with Time reversal invariance :

25. Perturbation theory in  em to 1  exchange gives no contribution to spin asymmetries spin asymmetries arise from interference between 1  exchange and absorptive part of 2  exchange

26. 2  exchange 1  exchange function of elastic nucleon form factors absorptive part of double virtual Compton scattering to De Rujula et al. (1971)

27. elastic contribution on-shell nucleon intermediate nucleon inelastic contribution resonant and non-resonant  N intermediate states calculated with MAID2003 : unitary isobar model X=  N all 13 **** resonances below 2 GeV included Drechsel, Hanstein, Kamalov, Tiator (1999)

28. Beam normal spin asymmetry N (elastic)  N (inelastic) total (N +  N) MAMI data F. Maas et al., PRL 94 (2005) New measurements at MAMI at backward angles : Pasquini & Vdh (2004) E e = 0.570 GeV for E e = 0.570 GeV B n = -8.59±0.89 ppm measurement of resonance form factors over range in Q 2

29. no suppression of B n with energy at fixed Q 2 x10 -6 p s (GeV) Q 2 = 0.05 GeV 2 B n in B n in diffractive region Afanasev & Merenkov Bn Bn Bn Bn σγpσγp E158 : B n = -3.5 -> -2.5 ppm (K. Kumar, prelim.) Note on SLAC E158 : 30% inelastic events included

30. Expt.E(GeV)θeθe Q 2 GeV 2 B n (ppm) SAMPLE0.1921460.10-16.4±5.9 A40.570350.11-8.59±0.89 A40.855350.23-8.52±2.31 HAPPEX3.0160.11-6.7 ± 1.5 G03.0190.15-4.06± 1.62 G03.0370.25-4.82 ± 2.85 E-158(ep)46.0~3.00.06-3.5 -> -2.5 E-158(ee)46.0~1000.03 Beam normal spin asymmetry : experiments

31. Elastic electron-nucleon amplitudes with electron helicity flip In Born approximation :

32. Elastic electron-quark amplitudes with electron helicity flip lepton mass new amplitude

33. Beam normal spin asymmetry : partonic calculation “magnetic” GPD “electric” GPD

34. Beam normal spin asymmetry : proton results Future PV experimental set-ups (0.1 ppm precision) : challenge to measure this asymmetry Results of GPD calculation Note : elastic contribution to Bn is negligibly small

35. Summary Normal spin asymmetries (NSA) in elastic electron-nucleon scattering : unique new tool to access the imaginary part of 2  exchange amplitudes -> Imaginary part of 2  amplitude absorptive part of non-forward doubly VCS tensor -> Unitarity to relate the absorptive part of doubly VCS tensor to pion-electroproduction amplitudes beam NSA in the resonance region as a new tool to extract resonance transition form factors -> In hard scattering region : use handbag approach to relate beam and target NSA to moments of GPDs difference Rosenbluth vs polarization data -> G E p /G M p : now mainly understood as due to two-photon exchange effects -> quantitative theoretical calculations needed -> precision test : several new expt. planned