Generalized parton distributions and gravitational form factors at large momentum transfer

TL;DR

This paper develops a SCET-based framework to resum large logarithms in GPDs at high momentum transfer, enabling precise predictions of form factors and revealing a new dominant power-law behavior in the $t$-dependence.

Contribution

It introduces a factorization theorem within SCET that resums Sudakov logarithms in GPDs at large $t$, and identifies a novel $ ext{order } ext{ extalpha}_s$ power-law $t$-dependence.

Findings

Resummation of Sudakov logarithms in GPDs at large $t$

Factorization of $x$-dependence of GPDs at large $t$

Discovery of a new $ ext{order } ext{ extalpha}_s$ power-law $t$-dependence

Abstract

Within the soft collinear effective theory (SCET), we derive a factorization theorem which resums Sudakov logarithms $(\alpha_s\ln^2(-t))^n$ to all orders in the quark-in-quark generalized parton distribution (GPD) at large momentum transfer $t$, and perform a consistency check to one-loop. We show that the same Sudakov factor appears in the `Feynman' contribution to the GPDs of the nucleon. Our result enables the resummation of all the large logarithms $\ln Q^2$ and $\ln^2t$ in exclusive processes with two hard scales $\Lambda_{\rm QCD}^2\ll |t| \ll Q^2$. We also present a SCET power counting analysis of the Feynman contributions to the GPDs and show that the $x$-dependence of GPDs factorizes at large-$t$ with controlled corrections. This in particular implies that any ratio of GPD moments such as the electromagnetic and gravitational form factors (GFF) is perturbatively calculable in this approximation. Furthermore, we identify a novel order $\alpha_s$ power-law $t$-dependence in the GPD and the $D$-type GFF that will dominate over the standard order $(\alpha_s^2)$ `leading twist' asymptotic contribution in the phenomenologically relevant region of $t$.