The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
D. de Florian, M. Grazzini
TL;DR
This work derives the structure of large logarithmic corrections at small transverse momentum in hadronic collisions up to next-to-next-to-leading logarithmic accuracy by leveraging the infrared behavior of tree-level and one-loop QCD amplitudes. It provides a general, process-dependent extraction of resummation coefficients for quark and gluon channels, including explicit results for Drell–Yan and Higgs production in the large m_top limit, and demonstrates that the conventional Sudakov form factor is not universal. By computing both real and virtual ${\cal O}(\alpha_s^2)$ contributions and matching to the q_T-resummation formalism, the authors obtain closed expressions for the NNLL coefficients $A^{(2)}$ and $B^{(2)F}$, with the latter containing a hard, process-dependent piece tied to the one-loop LO amplitude. The findings motivate an improved resummation framework with a process-dependent hard function $H_c^{F}$ to restore universality, and have practical impact for more precise matching of resummed and fixed-order predictions, especially in Higgs production and related processes.
Abstract
We consider the region of small transverse momenta in the production of high-mass systems in hadronic collisions. By using the current knowledge on the infrared behaviour of tree-level and one-loop QCD amplitudes at O(alpha_s^2), we analytically compute the general form of the logarithmically-enhanced contributions up to next-to-next-to-leading logarithmic accuracy. By comparing the results with q_T-resummation formulae we extract the coefficients that control the resummation of the large logarithmic contributions for both quark and gluon channels. Our results show that within the conventional resummation formalism the Sudakov form factor is actually process-dependent.