Subleading power factorization with radiative functions

Ian Moult,Iain W Stewart,Gherardo Vita

doi:10.1007/jhep11(2019)153

Abstract

The study of amplitudes and cross sections in the soft and collinear limits allows for an understanding of their all orders behavior, and the identification of universal structures. At leading power soft emissions are eikonal, and described by Wilson lines. Beyond leading power the eikonal approximation breaks down, soft fermions must be added, and soft radiation resolves the nature of the energetic partons from which they were emitted. For both subleading power soft gluon and quark emissions, we use the soft collinear effective theory (SCET) to derive an all orders gauge invariant bare factorization, at both amplitude and cross section level. This yields universal multilocal matrix elements, which we refer to as radiative functions. These appear from subleading power Lagrangians inserted along the lightcone which dress the leading power Wilson lines. The use of SCET enables us to determine the complete set of radiative functions that appear to mathcal{O} (λ2) in the power expansion, to all orders in αs. For the particular case of event shape observables in e+e−→ dijets we derive how the radiative functions contribute to the factorized cross section to mathcal{O} (λ2).

Highlights

The simplicity of the soft and collinear limits of gauge theories allows for an all orders understanding of the behavior of amplitudes and cross sections, typically formulated in terms of factorization theorems [1,2,3]
Unlike for observables which are amenable to a local operator product expansion (OPE) [4], these general factorization theorems typically involve non-local matrix elements with Wilson lines
Gauge invariance is guaranteed by an intricate Wilson line structure, dictated by the symmetries of the effective theory. We show how these radiative functions appear in factorization formulas at subleading power, both at the level of the amplitude and the cross section, as multilocal matrix elements with convolutions of operators along the lightcone

Summary

Introduction

The simplicity of the soft and collinear limits of gauge theories allows for an all orders understanding of the behavior of amplitudes and cross sections, typically formulated in terms of factorization theorems [1,2,3]. SCET has been used to systematically study power corrections to the leading power factorization for B → Xsγ, B → Xulν [13, 14] in the shape function region [15,16,17], and derive subleading factorization theorems in terms of universal non-local operators [8, 9, 18,19,20,21,22,23]. The power corrections take the form of non-local operators describing both soft fluctuations at the scale ΛQCD, in terms of matrix elements of the B meson, as well as the coupling of soft and collinear modes

Objectives

Discussion

Conclusion