Factorization at subleading power, Sudakov resummation, and endpoint divergences in soft-collinear effective theory

Ze Long Liu,Matthias Neubert,Bianka Mecaj,Xing Wang

doi:10.1103/physrevd.104.014004

Abstract

Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $h\to\gamma\gamma$ decay of the Higgs boson, for which we resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order. We also briefly discuss the related $gg\to h$ amplitude.

Highlights

Soft-collinear effective theory (SCET) [1,2,3] provides an efficient framework for addressing the problem of scale separation for cross sections and decay rates in high-energy physics
Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory
Based on a renormalized SCET factorization theorem for an observable appearing at subleading power in the ratio of two hierarchical mass scales m ≪ M, in which endpointdivergent convolution integrals are regularized by plus-type subtractions and the use of exact D-dimensional refactorization conditions, we have performed the first resummation of Sudakov logarithms for a subleading-power quantity (T3) in RG-improved perturbation theory

Summary

INTRODUCTION

Soft-collinear effective theory (SCET) [1,2,3] provides an efficient framework for addressing the problem of scale separation for cross sections and decay rates in high-energy physics. The “bare” factorization formula for the decay amplitude contains three terms consisting of unrenormalized SCET operators multiplied by bare Wilson coefficients, which account for the hard matching corrections arising when the “full theory” (the Standard Model with top quarks integrated out) is matched onto SCET. The third operator consists of the time-ordered product of the scalar Higgs current with two subleading-power terms in the SCET Lagrangian, in which hard-collinear fields are coupled to a soft quark field. It arises from full-theory graphs containing a soft quark propagator between the two photons, with all momentum components of order mb. We briefly discuss the extension of our approach to the related gg → h process, showing that the presence of colored particles in the initial state does not pose any new difficulties

FACTORIZATION WITH ENDPOINT DIVERGENCES

SUDAKOV RESUMMATION AT SUBLEADING POWER AND NLL ORDER

Findings

CONCLUSIONS AND OUTLOOK