Deeply virtual Compton scattering amplitude at the tree level: Transversality, twist-3, and factorization

Abstract

We study the virtual Compton amplitude in the generalized Bjorken region (q 2 → ∞, t small) in QCD by means of a light-cone expansion of the product of e.m. currents in string operators in coordinate space. Electromagnetic gauge invariance (transversality) is maintained by including in addition to the twist-2 operators "kinematical" twist-3 operators which appear as total derivatives of twist-2 operators. The non-forward matrix elements of the elementary twist-2 operators are parametrized in terms of two-variable spectral functions (double distributions), from which twist-2 and 3 skewed distributions are obtained through reduction formulas. Our approach is equivalent to a Wandzura-Wilczek-type approximation for the twist-3 skewed distributions. The resulting Compton amplitude is manifestly transverse up to terms of order t/q 2 . We find that in this approximation the tensor amplitude for longitudinal polarization of the virtual photon is finite, while the one for transverse polarization contains a divergence already at tree level. However, this divergence has zero projection on the polarization vector of the final photon, so that the physical helicity amplitudes are finite.

Kinematical Issues in the GPD Formulation of DVCS

“…In our more general kinematics K 4 we thus find for T s (see also Vanderhaegen et al [6][7][8][9][10][11] where transversemomentum components are included)…”

“…The inclusion of higher twist effects [6][7][8][9][10][11]15] is at the current forefront of research and it may well go beyond the handbag approximation.…”

Spin-polarized high-energy scattering of charged leptons on nucleons

“…DVCS ep → epγ , has two advantages: (i) among the hard exclusive processes that can be accessed experimentally in the foreseeable future, it is considered to be the one with the most reliable theoretical interpretation; (ii) effects of NLO [173][174][175] and subleading twist (see section 1) corrections [176][177][178] are under theoretical control. For suitably chosen observables the lowest correction is of order 1/Q 2 instead of 1/Q.…”

Finite-t and target mass corrections in off-forward hard reactions

“…The separation of kinematic corrections ∝ t/Q 2 from generic twist-four corrections O(Λ 2 QCD /Q 2 ) proves, however, to be surprisingly difficult. The problem is well known and its importance for phenomenology has been acknowledged by many authors [4,5,6,7,8,9,10,11,12,13].…”