Rapidity Logarithms in SCET Without Modes

TL;DR

This paper revisits rapidity divergences in Soft-Collinear Effective Theory without explicit modes, deriving rapidity renormalization group equations and demonstrating factorization in key processes.

Contribution

It introduces a mode-independent formulation of SCET that handles rapidity divergences through scheme dependence and derives associated renormalization group equations.

Findings

Rapidity divergences lead to scheme dependence in the effective theory.

Rapidity renormalization group equations are derived from scheme dependence.

Rates factorize into hard, soft, and jet contributions without explicit modes.

Abstract

We re-examine observables with rapidity divergences in the context of a formulation of Soft-Collinear Effective Theory in which infrared degrees of freedom are not explicitly separated into modes. We consider the Sudakov form factor with a massive vector boson and Drell-Yan production of lepton pairs at small transverse momentum as demonstrative examples. In this formalism, rapidity divergences introduce a scheme dependence into the effective theory and are associated with large logarithms appearing in the soft matching conditions. This scheme dependence may be used to derive the corresponding rapidity renormalization group equations, and rates naturally factorize into hard, soft and jet contributions without the introduction of explicit modes.