Resummation of threshold logarithms in deeply-virtual Compton scattering

TL;DR

This paper develops an all-order resummation formula for threshold logarithms in deeply-virtual Compton scattering, improving theoretical precision at NNLL accuracy and showing that resummation effects are likely small.

Contribution

It introduces a novel resummation method for logarithmic enhancements in the quark coefficient function at NNLL accuracy using factorization and renormalization group equations.

Findings

Resummation formula derived at NNLL accuracy.

Factorization of the coefficient function in the x → ±ξ limit.

Preliminary analysis indicates small resummation corrections.

Abstract

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to $\frac{\alpha_s^n}{x \pm \xi} \log (\frac{\xi \pm x}{2\xi})^k$ in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the $x \rightarrow \pm \xi$ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.