Compton scattering: From deeply virtual to quasi-real

Abstract

We address the question of interpolation of the virtual Compton scattering process off a polarized nucleon target between the deeply virtual regime for the initial-state photon and its near on-shell kinematics making use of the photon helicity-dependent Compton Form Factors (CFFs) as a main ingredient of the formalism. The five-fold differential cross section 1 for the reaction with all possible polarization options for the lepton and nucleon spins is evaluated in terms of CFFs in the rest reference frame of the initial-state nucleon. We suggest a rather simple parametrization of the Compton hadronic tensor in terms of CFFs which are free from kinematical singularities and are directly related, at large photon virtualities, to Generalized Parton Distributions. We also provide a relation of our basis spanned by a minimal number of Dirac bilinears to the one introduced by Tarrach for the parametrization of the virtual Compton tensor and utilize the former to establish a set of equalities among our CFFs and Generalized Polarizabilities. As a complementary result, we express Compton scattering in the Born approximation in terms of CFFs as well.

GPD phenomenology and DVCS fitting

“…They were followed by numerous dedicated experiments [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] during a period of intense theoretical activity which put DVCS under solid control. In particular let us mention the full description of DVCS up to twist-3 [27,28,29,30], including the discussion of QED gauge invariance [31,32,33,34] and target mass and finite momentum transfer corrections [35,36], the computation of higher orders in the perturbative expansion in the strong running coupling [37,38,39,40,41,42,43,44,45,46], and the soft-collinear resummation of DVCS [47,48]. Two closely related processes, Timelike Compton Scattering (TCS) [49,50] and Double Deeply Virtual Compton Scattering (DDVCS) [51,52,…”

“…Detailed expressions for the coefficients c n and s n are given in refs. [27,28,29,30], labeled BMK. Note that the cross section in eq.…”

J=0fixed pole andD-term form factor in deeply virtual Compton scattering

“…This task certainly provides further motivation to build up a unique framework for Compton scattering from real to the deeply virtual regime, launched in [25]. However, employing the GPD sum rule for the D-term form factor requires the theoretical extrapolation of experimental measurements into the high energy asymptotic regime.…”

PARTONS: PARtonic Tomography Of Nucleon Software

“…During the same period, an intense theoretical activity put DVCS under solid control. In particular we mention the full description of DVCS up to twist-3 [50][51][52][53], the computation of higher orders in the perturbative QCD expansion [54][55][56][57][58][59][60][61][62][63], the softcollinear resummation of DVCS [64,65], the discussion of QED gauge invariance [66][67][68][69][70] and the elucidation of finite-t and target mass corrections [71,72]. Variety of those existing theoretical improvements, usually developed within the model/framework preferred by the corresponding authors, also justify the need for a common framework enabling systematic comparisons.…”

“…[75,107], and the latest set of expressions [53] by Belitsky and Müller. Alpha Four-loop perturbative running of the strong coupling constant from PDG [108], and constant value.…”