The Infrared Structure of Perturbative Gauge Theories

Abstract

Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders.

A Deformed Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory

“…by adding these two contributions. 15 We can analyze the action of ∂z1 ∂z2 appearing at the end of (3.18) by taking the procedures in the footnote 12 and the footnote 14.…”

“…In [8], the supersymmetric w 1+∞ algebra has been identified with the corresponding soft current algebra in the supersymmetric Einstein-Yang-Mills theory. The relevant works on the celestial holography in the various directions can be found in [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. See [1] for more complete literatures.…”

Power suppressed corrections show new features of infrared cancellations

“…( 7), we use the fictitious photon mass λ ≡ Q while the electron mass is m ψ ≡ ψ Q. 1 After doing the trace, the structure [ pol Z ρ (q) * σ (q)]T ρσ contains two kind of terms. The first kind does not depend on the integral variable k; Q 4 is one of those terms for instance.…”

“…In second place, finite observables feature, as a remnant of IR divergences, large logarithms that threaten to spoil the convergence of the perturbative series. It is then necessary to calculate higher orders contributions and/or perform an all-order resummation of leading terms (see [1] for a collection of the main references). In the Standard Model (SM), in the case of QED and QCD, one loop leading IR radiative correction are proportional to α log 2 (Q/λ), Q being a typical energy scale of the observable under consideration and λ an IR cutoff (for instance a fictitious photon mass).…”

“…We get the expressions both for virtual and real photon emission and we elucidate the way the cancellation of the IR divergence works including also the power suppressed terms. In section IV, we use our toy model based on U (1) ⊗ U (1) to study the interplay between various decay channels needed to ensure the cancellation of the power suppressed leading log corrections. The chiral character of the abelian gauge groups results important to emphasize the full generality of the mechanism of the various cancellations.…”