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


Catani, Stefano; de Florian, Daniel; Devoto, Simone; Grazzini, Massimiliano; Mazzitelli, Javier (2023). Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders. Journal of High Energy Physics, 2023(11):217.

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 β 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 α$_{S}$. In d = 4 dimensions we obtain the explicit relation between the soft couplings at $$ \mathcal{O} $$($$ {\alpha}_{\textrm{S}}^3 $$). 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.

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 β 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 α$_{S}$. In d = 4 dimensions we obtain the explicit relation between the soft couplings at $$ \mathcal{O} $$($$ {\alpha}_{\textrm{S}}^3 $$). 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Uncontrolled Keywords:Nuclear and High Energy Physics
Language:English
Date:29 November 2023
Deposited On:22 Dec 2023 12:57
Last Modified:28 Jun 2024 03:31
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/jhep11(2023)217
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)