Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders

Author:

Stefano Catani, Daniel de Florian, Simone Devoto, Massimiliano Grazzini, Javier Mazzitelli

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th)

journal:

TIF-UNIMI-2023-26, ZU-TH 52/23, PSI-PR-23-36

date:

2023-09-19 16:00:00

Abstract

We consider extensions of the soft-gluon effective coupling that generalize the Catani--Marchesini--Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD $\beta$ function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling $\alpha_s$. In d=4 dimensions we obtain the explicit relation between the soft couplings at ${\cal O}(\alpha_s^3).$ Finally, we study the structure of the soft coupling in the large-$n_F$ limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-$n_F$ results agree with the known result of the cusp anomalous dimension.

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