Sudakov Resummation for Prompt-Photon Production in Hadron Collisions
S. Catani, M. L. Mangano, P. Nason
TL;DR
The paper addresses the need for reliable predictions of prompt-photon production near threshold, where Sudakov logarithms become large. It derives explicit NLL Sudakov resummation formulas in Mellin space, showing fragmentation does not contribute at this order and the cross section factorizes into independent initial- and final-state radiators plus a soft-interference term. The authors provide detailed expressions for radiative factors and constant terms, and discuss their relation to color coherence and interferences, linking the prompt-photon case to Drell-Yan and DIS results. This framework enables precise phenomenology and uniform NLL global fits of parton densities in the large-$x$ region, with ready-to-use Mellin-space formulas and inverse transforms for practical applications.
Abstract
We present the explicit expressions for the resummation of large-x Sudakov effects in the transverse-energy distribution of prompt-photons produced in hadronic collisions, to next-to-leading logarithmic (NLL) accuracy. Fragmentation processes do not contribute to the Sudakov resummation at NLL level. In Mellin space, the resummed radiative factor factorizes in the product of independent radiators for the two initial and the one final coloured partons appearing in the Born process, times a simple factor describing the soft-gluon interferences between initial and final states. The formulae are given in terms of Mellin moments, and can be used for phenomenological applications using standard techniques for the inverse-Mellin transforms. The calculations presented in this work, when added to the existing works on DY and DIS production, complete the theoretical ground-work necessary to carry out global fits of parton densities with a uniform NLL accuracy in the large-x region.