Renormalization group approach to Sudakov resummation in prompt photon production

TL;DR

The paper addresses the challenge of resumming soft Sudakov logarithms in prompt photon production, where the kinematics introduce three scales and three potential sources of factorization violation. It generalizes a renormalization-group–based approach from Drell–Yan and DIS to the prompt-photon case, showing that soft logs can be organized in terms of $\alpha_s$ evaluated at $Q^2$, $Q^2/N$, and $Q^2/N^2$, and that the resummed cross section can be constructed from the physical anomalous dimension $\gamma(N,\alpha_s)$. The authors discuss three levels of factorization (full, weaker, none), detailing how many resummation coefficients $g_{mnp}$ must be determined and how fixed-order input grows with the desired logarithmic accuracy, highlighting that prompt-photon resummation is less predictive but more general than earlier results. They also emphasize that the framework can accommodate violations of Sudakov factorization and call for higher-order fixed-order calculations (e.g., $\mathcal{O}(\alpha_s^3)$) to test the various factorization scenarios.

Abstract

We prove the all-order exponentiation of soft logarithmic corrections to prompt photon production in hadronic collisions, by generalizing an approach previously developed in the context of Drell-Yan production and deep-inelastic scattering. We show that all large logs in the soft limit can be expressed in terms of two dimensionful variables, and we use the renormalization group to resum them. The resummed results that we obtain are more general though less predictive than those proposed by other groups, in that they can accommodate for violations of Sudakov factorization.