Abstract
Abstract We calculate the quark coefficient function T q (x, ξ) that enters the factorized amplitude for deeply virtual Compton scattering (DVCS) at all order in a soft and collinear gluon approximation, focusing on the leading double logarithmic behavior in (x±ξ), where x ± ξ is the light cone momentum fraction of the incoming/outgoing quarks. We show that the dominant part of the known one loop result can be understood in an axial gauge as the result of a semi-eikonal approximation to the box diagram. We then derive an all order result for the leading contribution of the ladder diagrams and deduce a resummation formula valid in the vicinity of the boundaries of the regions defining the energy flows of the incoming/outcoming quarks, i.e. x = ±ξ. The resummed series results in a simple closed expression.
Highlights
For hard electroproduction of mesons [21–24] and their timelike crossed versions, namely exclusive lepton pair production in photon or meson collisions with protons [25–27]
The aim of this paper is to study in detail the emergence of the leading logarithmic contributions near the points x = ±ξ, namely terms like [αsn log2n(ξ − x)]/(x − ξ) and [αsn log2n(ξ + x)]/(x + ξ), and to derive a resummed formula for the coefficient function of deeply virtual Compton scattering (DVCS)
Let us just remind the reader that the region x = ±ξ is crucial in the determination of beam spin asymmetries
Summary
We analyze the one-loop diagrams in details without making any approximation to understand which diagrams give contribution at order [αs log2(ξ − x)]/(x − ξ) and which give less singular contributions in light-like gauge. We explicitly show that the net contribution to [log2(ξ − x)]/(x − ξ) terms arises from the box-diagram in the case of cutting the gluonic line. This analysis precisely identifies the part of the phase space that is responsible for this contribution. One can write the integral for the left-vertex as IL.V. Let us calculate the numerator for the box diagram, illustrated, which is (Num)box = tr p/2γν k/ + (x − ξ)p/2 γ⊥σ k/ + p/1 + (x − ξ)p/2 γ⊥σ k/ + (x + ξ)p/2 γμ (2.13). Each of these two diagrams which involve cutting the fermionic line lead to log2(ξ − x)/(x − ξ) terms, but this type of contributions add to zero at the end. This rule will be extended later after studying in detail the two-loop contributions
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