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Normal spin asymmetries and two-photon processes : theory

This presentation discusses the theory and analysis of two-photon exchange processes in elastic electron-nucleon scattering. It explores the puzzle of different results obtained for the magnetic and electric form factors in Rosenbluth versus polarization experiments. The presentation explores beam and target normal spin asymmetry and the absorptive part of the double Virtual Compton Scattering amplitude. It also discusses the contribution of two-photon exchange effects to the Rosenbluth and polarization transfer measurements of the proton's form factors.

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Normal spin asymmetries and two-photon processes : theory

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  1. Normal spin asymmetries and two-photon processes :theory Marc Vanderhaeghen College of William & Mary / Jefferson Lab PAVI06 workshop, Milos, Greece, May 16 - 20, 2006

  2. Outline • Elastic eN scattering beyond the one-photon exchange approximation puzzle of different results extracted for GE/GM 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) • Z box processes to PV elastic eN scattering in coll. withA.Afanasev, S. Brodsky, C. Carlson, Y.C. Chen, M. Gorchtein, P.A.M. Guichon, V. Pascalutsa, B. Pasquini

  3. Two-photon exchange effects Rosenbluth vs polarization transfer measurements of GE/GM of proton SLAC, Jlab Rosenbluth data Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002) Twomethods, twodifferentresults !

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

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

  6. 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 Q2

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

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

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

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

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

  12. with • Time reversal invariance : Unitarity

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

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

  15. lepton hadron Hadronic Tensor: Absorptive part of Doubly Virtual Compton Tensor q q P P n n X on-shell intermediate states (MX2 = W2) Transverse spin asymmetries • Beam normal spin asymm. • Target normal spin asymm. sum over spins unpolarized particles

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

  17. ' ' (near) collinear singularities Q21' 0, Q22 0 Quasi - VCS k // k1 Q21 0, Q22'0 ' Quasi - VCS k1 // k’ Q21' 0, Q22' 0 Quasi - RCS k1 = 0, W = ps – me

  18. Kinematical bounds for Q12 and Q22 Elastic contribution Inelastic contribution

  19. Phase space integration ‘Soft’ intermediate electron; Both photons are hard collinear • 2-dim integration (Q12, Q22) for the elastic intermediate state • 3-dim integration (Q12, Q22,W2) for inelastic excitations MAMI A4 E = 855 MeV Θcm= 57 deg SAMPLE E =200 MeV One photon is Hard collinear

  20. N (inelastic) tot (N +  N) N (elastic) SAMPLE data Wells et al., PRC (2001) Quasi-RCS peak 0 p + n tot Beam normal spin asymmetry Ee = 0.2 GeV Integrand [ppm GeV-1] Pasquini & Vdh (2004) • inelastic contribution dominated by the region of threshold pion production • MAID in the threshold region is consistent with chiral predictions

  21. Recoil corrections to scattering from point charge Nucleon charge radius Nucleon isovector magnetic moment SAMPLE data S. Wells et al. (2001) Beam normal spin asymmetry : Ee = 0.2 GeV Diaconescu & Ramsey-Musolf (2004) EFT calculation : to second order in Ee /MN Pions are integrated out calculation includes : NLO LO

  22. + n 0p Beam normal spin asymmetry: energy dependence at fixed cm=120o full calculation quasi-RCS approximation

  23. MAMI data F. Maas et al., PRL 94 (2005) N (elastic) total (N +  N) N (inelastic) Beam normal spin asymmetry Pasquini & Vdh (2004) for Ee = 0.570 GeV Bn = -8.59±0.89 ppm talk :L. Capozza New measurements at MAMI at backward angles :

  24. Integrand : beam normal spin asymmetry Ee = 0.855 GeV D13 (1520)  (1232) 0 p + n tot Quasi-RCS peak

  25. Beam normal spin asymmetry Ee = 0.570 GeV Proton Neutron N (inelastic) N (elastic) total

  26. N -> Δtransition form factors in large Nc limit modified Regge model measurement of NΔ magnetic form factor over range of Q2 Regge model

  27. ' Bn at high energy & forward angle forward region (q -> 0) : dominated by near collinear singularity • Q21' 0, Q22' 0, W = ps – me • Quasi RCS p total cross section Log enhancement Afanasev & Merenkov : PRD 70 (2004) 073002 corrected result given by : Gorchtein : PRC 73 (2006) 035213

  28. x10-6 Bn Bn in diffractive region Q2 = 0.05 GeV2 E158 : Bn = -3.5 -> -2.5 ppm (K. Kumar, prelim.) no suppression of Bn with energy at fixed Q2 ps (GeV) Afanasev & Merenkov σγp Note on SLAC E158 : 30% inelastic events included

  29. Bn in diffractive region Ee ( in GeV ) 45 : SLAC E158 E158 : Bn = -3.5 -> -2.5 ppm (K. Kumar, prelim.) 12 6 3 Gorchtein

  30. intermediate energies & forward angles • dominance of collinear-photon exchange => • replace 3-dim integral over (Q12,Q22,W) with 1-dim integral along the line : Q12 ≈ 0 ; Q22 = Q2 (s-W2) / (s-M2) Afanasev & Merenkov used σγpfrom parameterization by N. Bianchi at al. (1996) for resonance region and Block&Halzen (2004) for high energy (Regge fit)

  31. Beam normal spin asymmetry : Ee = 3 GeV Afanasev & Merenkov approximate hadronic tensor by forward limit and use fit to experimental data on σγp data also expected fromG0 HAPPEX talk :L. Kaufmann

  32. Quasi-RCS peak 0 p + n tot Bn: resonance contribution ( no forward approx. ) Ee = 3 GeV Wmax= 2. GeV (MAID2000) HAPPEX integration up to Wmax= 2.5 GeV (MAID2003) Integrand [ppm GeV-1] F15 (1680)  (1232) D13 (1520) Pasquini & Vdh Additional contributions like 2-pion intermediates states become important

  33. Beam normal spin asymmetry : experiments

  34. Target normal spin asymmetry Ee = 0.570 GeV Proton Neutron % N (inelastic) N (elastic) total

  35. Integrand : target normal spin asymmetry Ee = 0.855 GeV Ee = 2 GeV N loops N loops D(1232) D(1232) 0 p + n tot

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

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

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

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

  40. Z box diagram processes to PV elastic eN scattering in coll. with C. Carlson, Y.C. Chen, V. Pascalutsa, B. Pasquini

  41. e e e e  Z p p p p e e 2  p p Strange Electric and Magnetic form factors, + Axial form factor PV electron scattering polarized electrons, unpolarized target V V, A A, V V At a given Q2, ranges from 1 (forward angle) to 0 (backward angle) Rosenbluth separation of strange form factors

  42. V  A e- helicity conservation Parity + Time reversal (or charge conjugation) 3 structures elastic eN scattering : general PV amplitude Kinematical invariants : contains 3 independent Invariant Amplitudes function of Q2, 

  43. e e e e V A V A p p p p e e e e V A V A V A V A p p p p leading order contribution to MPV beyond the leading order

  44. Hadronic corrections at backward angles ( intermediate Q2 )  Z0 + 2 diagrams with  and Z interchanged calculation in forward kinematics (APV) exists :Marciano & Sirlin (1984) in non-forward kinematics : more tensor structures & form factors effects check results with quark-parton model calculation : Bohm & Spiesberger (1986, 1987)

  45. lepton tensors hadron tensors

  46. 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

  47. Many thanks to the organizers !

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