Resummation of threshold logarithms in deeply-virtual Compton scattering

Abstract

Abstract I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to $$ \frac{\alpha_s^n}{x\pm \xi } $$ α s n x ± ξ log $$ {\left(\frac{\xi \pm x}{2\xi}\right)}^k $$ ξ ± x 2 ξ 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 → ±ξ 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.