Renormalization and Scale Evolution of the Soft-Quark Soft Function

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 $h\to \gamma \gamma$ process mediated by light-quark loops. We perform the renormalization of this soft function at one-loop order, derive 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 multiplicative.

30 pages plus appendices and references, 6 figures

References in corpus (28)

• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Hard Scattering Factorization from Effective Field Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Asymptotics of Heavy-Meson Form Factors
• Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering
• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• Threshold Resummation in Momentum Space from Effective Field Theory
• The Quark Form Factor at Higher Orders
• Reparameterization Invariance for Collinear Operators
• Renormalization-Group Evolution of the B-Meson Light-Cone Distribution Amplitude
• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
• Model-Independent Properties of the B-Meson Distribution Amplitude
• Factorization and Sudakov Resummation in Leptonic Radiative B Decay
• High-Energy Limit of QCD beyond Sudakov Approximation
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Subleading Power Factorization with Radiative Functions
• High-Energy Limit of Mass-Suppressed Amplitudes in Gauge Theories
• Advanced Predictions for Moments of the B->X_s+gamma Photon Spectrum
• The Soft Quark Sudakov
• Two-loop evolution equation for the B-meson distribution amplitude
• Conformal symmetry of the Lange-Neubert evolution equation
• Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays
• On the resummation of double logarithms in the process Higgs --> two photons
• On the Resummation of Large QCD Logarithms in Higgs -> 2 Photons Decay

Cited by in corpus (19)

• 50 Years of Quantum Chromodynamics
• Factorization at Subleading Power, Sudakov Resummation and Endpoint Divergences in Soft-Collinear Effective Theory
• Factorization at Subleading Power and Endpoint Divergences in $h\to \gamma \gamma$ Decay: II. Renormalization and Scale Evolution
• Towards all-order factorization of QED amplitudes at next-to-leading power
• Factorization at Next-to-Leading Power and Endpoint Divergences in $gg\to h$ Production
• Next-to-leading power threshold corrections for finite order and resummed colour-singlet cross sections
• Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space
• Radiative Quark Jet Function with an External Gluon
• Light-cone distribution amplitudes of heavy mesons with QED effects
• Threshold resummation of new partonic channels at next-to-leading power
• Light-cone distribution amplitudes of light mesons with QED effects
• Systematic Parametrization of the Leading $B$-meson Light-Cone Distribution Amplitude
• Threshold factorization of the Drell-Yan quark-gluon channel and two-loop soft function at next-to-leading power
• Renormalization of the radiative jet function
• Analyticity, renormalization, and evolution of the soft-quark function
• Renormalization of the next-to-leading-power $\gamma \gamma \to h$ and $gg\to h$ soft quark functions
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Renormalisation group evolution of the shape function $g_{17}$ in $\bar{B}\to X_s\gamma$ and $\bar{B}\to X_s{\ell }^{+}{\ell }^{-}$ at subleading power
• Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold