Renormalization of the next-to-leading-power $\gamma \gamma \to h$ and $gg\to h$ soft quark functions

Abstract

We calculate directly in position space the one-loop renormalization kernels of the soft operators $O_{\gamma }$ and $O_g$ that appear in the soft-quark contributions to, respectively, the subleading-power $\gamma \gamma \to h$ and $gg\to h$ form factors mediated by the $b$-quark. We present an IR/rapidity divergence-free definition for $O_g$ and demonstrate that with a correspondent definition of the collinear function, a consistent factorization theorem is recovered. Using conformal symmetry techniques, we establish a relation between the evolution kernels of the leading-twist heavy-light light-ray operator, whose matrix element defines the $B$-meson light-cone distribution amplitude (LCDA), and $O_{\gamma }$ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of $O_{\gamma }$ to the two-loop level. We construct an ansatz for the kernel of $O_g$ at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant.

arXiv commentjournal version

References in corpus (40)

• An effective field theory for collinear and soft gluons: heavy to light decays
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• Infrared singularities of scattering amplitudes in perturbative QCD
• The Uses of Conformal Symmetry in QCD
• Multipole-expanded soft-collinear effective theory with non-abelian gauge symmetry
• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• The B-Meson Distribution Amplitude in QCD
• Infrared singularities of QCD amplitudes with massive partons
• Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Power-enhanced leading-logarithmic QED corrections to $B_q\to {\mu }^{+}{\mu }^{-}$
• Renormalization-Group Evolution of the B-Meson Light-Cone Distribution Amplitude
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
• Subleading Shape Functions in Inclusive B Decays
• Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power
• Factorization for Power Corrections to B->Xs gamma and B-> Xu e nu
• First Subleading Power Resummation for Event Shapes
• Higher-twist B-meson Distribution Amplitudes in HQET
• Anomalous dimension of subleading-power $N$-jet operators II
• Threshold factorization of the Drell-Yan process at next-to-leading power
• Power corrections to B\to X_u l ν(X_sγ) decay spectra in the "shape-function" region
• Leading-logarithmic threshold resummation of Higgs production in gluon fusion at next-to-leading power
• Quantum mechanics of null polygonal Wilson loops
• Evolution equations beyond one loop from conformal symmetry
• Two-loop evolution equation for the B-meson distribution amplitude
• Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization
• Conformal symmetry of the Lange-Neubert evolution equation
• Factorization at Subleading Power and Endpoint Divergences in $h\to \gamma \gamma$ Decay: II. Renormalization and Scale Evolution
• Two-loop conformal generators for leading-twist operators in QCD
• Renormalization and Scale Evolution of the Soft-Quark Soft Function
• Factorization at Next-to-Leading Power and Endpoint Divergences in $gg\to h$ Production
• Gauge theory webs and surfaces
• Relating amplitude and PDF factorisation through Wilson-line geometries
• QED factorization of non-leptonic $B$ decays
• Evolution equation for the higher-twist B-meson distribution amplitude
• Integrability in heavy quark effective theory
• Threshold factorization of the Drell-Yan quark-gluon channel and two-loop soft function at next-to-leading power
• Analyticity, renormalization, and evolution of the soft-quark function

Cited by in corpus (2)

• 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
• Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets