Two Photon Exchange in Inclusive and Semi Inclusive DIS Marc Schlegel Theory Center, Jefferson Lab In collaboration with Christian Weiss, Andrei Afanasev, Andreas Metz
Two Photon Exchange in elastic scattering Most prominent example: Form Factor measurements Two extraction methods: Rosenbluth Method Discrepancy of G M /G E in OPE! Polarization transfer method TPE suggest to resolve discrepancy [Guichon, Vanderhaeghen,2003] Two Photon Exchange (TPE): Parton GPD Model: [Chen et al., PRL 93, 122301] TPE generates Single Spin Asymmetries (SSA)!
TPE in inclusive DIS SSA in incl. DIS forbidden on general grounds for One Photon Exchange Time reversal (Christ Lee, 1966) confirmed by a SLAC experiment in 1970, up to 3.5 % level new JLab experiment E 07 013, up to 10 4 Two Photon Exchange allows Single Spin Asymmetries: naive Parton Model calculation [Metz, M.S., Goeke, Phys. Lett. B 643, 2006] coupling to the same parton, 1/Q expansion
1) Transverse Beam SSA: Leading twist PDF, no collinear / IR divergences. Proportional to lepton mass and 10 6 10 5 Muons? 2) Transverse Target SSA: Subleading twist PDF g T, proportional to nucleon mass, not quark mass. Collinear divergence in the naïve parton model, e.m. gauge invariance not preserved Cancellation beyond naïve parton model, multi parton correlations situation similar to one photon exchange
3) Beyond the naïve parton model: Try handbag approach with k T dependent PDFs (TMDs): Collinear divergence remains, but QCD equation of motion applicable. Quark gluon correlation might cancel coll. Div., restore e.m. gauge invariance. What if not... multi quark correlations? [Afanasev, Weiss, Strikman, PRD 77, 014028]: argue that multi quark correlations play no role. suggest other mechanism: Quark helicity flip due to interaction with non pert. QCD vacuum, m q m q,const.
TPE in Semi Inclusive DIS Naïve parton model calculations of SSA due to TPE: Longitudinal Beam Polarization: One new structure function ~sin(2 ) Leading twist asymmetry, free of collinear / IR divergences. Recovery of the Boer Mulders effect Target polarization (long. and transverse): naïve parton model collinearly divergent contributions to twist 3 asymmetries Evidences: TPE corrections to Sivers Asymmetry even twist 4.
Model Calculations of transv. SSA [Afanasev, Weiss, Strikman, PRD 77, 014028] Model of a point like nucleon: IR / collinear divergences cancel SSA proportional to nucleon mass SSA of order 10 3 10 4 Constituent Quark Model of the nucleon: SSA > 0 for a proton SSA < 0 for a neutron
Scalar Diquark Spectator Model with C. Weiss, A. Afanasev Investigate the Transverse Target SSA in a dynamical model estimate of the size & study of cancellation of divergences Field theoretical model with Yukawa interaction: Unpolarized Cross Section: Consider neutron target photon parton coupling only E.M. Gauge invariance: coupling to diquark necessary (e q = e dq ) Assume d quark dominance
Fitting the parameters Compute unpolarized model cross section: Phase space integration in the photon neutron c.m. frame Improvement of the model restriction of the phase space No intrinsic soft scale in this model Usually: Pheno. Form Factors at N q dq vertex by hand But: F.F.s violate e.m. gauge invariance x B dependent Gaussian width: E.M. gauge invariance preserved, allows better fit to parton model
Comparison with CTEQ5 PDF parameterisation:
Transverse Target SSA Transverse Target SSA due to TPE: TPE diagrams (including an imaginary part): Two diagrams compatible with parton model, two are beyond. All diagrams needed to ensure e.m. gauge invariance, even at leading twist (1/Q expansion) cancellation of collinear divergences.
Technical simplifications: Diagrams can be grouped, each group alone is e.m. gauge invariant, e.g. Loop integral is of the form functions easily evaluated in the outgoing lepton quark c.m. frame Boost of the loop momentum SSA: 2 angular integrals + phase space integral 4 dim. integral
SSA of order 10 4 10 3, in agreement with Const. Quark Model. However: Sign is opposite in this model for a neutron.
Summary Two Photon Exchange generates SSAs in incl. and semi incl. DIS naïve Parton Model: Inclusive DIS: Transverse Beam SSA: free of divergences, leading twist Transverse Target SSA: collinear divergences, subleading twist restore e.m. gauge invariance multi parton correlations Semi inclusive DIS: TPE generates a new observable Boer Mulders effect in beam SSA. Estimate of the Transverse Target SSA in DIS: scalar diquark model study of the cancellation of divergences Asymmetry > 0 for a neutron, and ~ 10 3 10 4