Double logarithms resummation in exclusive processes : the surprising behavior of DVCS

TL;DR

This paper investigates the resummation of double logarithms in Deeply Virtual Compton Scattering (DVCS), revealing a novel non-alternating series pattern that can be summed into a hyperbolic cosine function, contrasting with previous results.

Contribution

It introduces a new resummation pattern for the DVCS quark coefficient function near x=ξ, showing a cosh resummation that differs from known behaviors in similar processes.

Findings

The coefficient function develops a non-alternate series in α_s^n log^{2n}(x-ξ).

Resummation leads to a cosh[K sqrt α_s log(x-ξ)] factor.

Contrasts with the behavior of the pion transition form factor near the endpoint.

Abstract

Double logarithms resummation has been much studied in inclusive as well as exclusive processes. The Sudakov mechanism has often be the crucial tool to exponentiate potentially large contributions to amplitudes or cross-sections near phase-space boundaries. We report on a recent work where a very different pattern emerges : the DVCS quark coefficient function C(x,\xi) develops, near the particular point x=\xi, a non-alternate series in \alpha_s^n log^{2n}(x-\xi) which may be resummed in a cosh[K sqrt \alpha_s log(x-\xi)] factor. This result is at odds with the known result for the corresponding coefficient function for the pion transition form factor near the end point C(z) although they are much related through a z -> x/\xi correspondence.