Abstract
Soft functions defined in terms of matrix elements of soft fields dressed by Wilson lines are central components of factorization theorems for cross sections and decay rates in collider and heavy-quark physics. While in many cases the relevant soft functions are defined in terms of gluon operators, at subleading order in power counting soft functions containing quark fields appear. We present a detailed discussion of the properties of the soft-quark soft function consisting of a quark propagator dressed by two finite-length Wilson lines connecting at one point. This function enters in the factorization theorem for the Higgs-boson decay amplitude of the h → γγ process mediated by light-quark loops. We perform the renormalization of this soft function at one-loop order, present a conjecture for its two-loop anomalous dimension and discuss solutions to its renormalization-group evolution equation in momentum space, in Laplace space and in the “diagonal space”, where the evolution is strictly local in the momentum variable.
Highlights
Soft-collinear effective theory (SCET) offers a convenient framework for analyzing the factorization properties of cross sections and scattering amplitudes sensitive to different, hierarchical scales [1,2,3,4]
In this work we have presented a detailed analysis of the renormalization and the scale evolution of the soft-quark soft function S(w, μ), defined in terms of the discontinuity of the soft quark propagator dressed by two finite-length Wilson lines connecting at one point
The results we have obtained and the techniques we have developed have a more general importance in the context of understanding SCET factorization theorems at subleading order in power counting, where soft functions containing soft quarks dressed by Wilson lines become a generic feature
Summary
Soft-collinear effective theory (SCET) offers a convenient framework for analyzing the factorization properties of cross sections and scattering amplitudes sensitive to different, hierarchical scales [1,2,3,4]. There has been a growing interest in understanding factorization at subleading power in scale ratios In this case a large number of hard, jet and soft functions appear. The Wilson lines Sn and Snconnect the soft quarks with the Higgs vertex and ensure that the matrix element is gauge invariant. To this end we generalize the concept of the “dual space” introduced in [10, 11] to higher orders of perturbation theory. Several technical details of our analysis are presented in three appendices
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