Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

TL;DR

This paper develops a novel resummation method for off-diagonal deep-inelastic scattering channels near threshold, overcoming divergence issues and deriving new all-order expressions for splitting functions using effective theory techniques.

Contribution

It introduces a $d$-dimensional consistency approach to resum NLP double logarithms in off-diagonal channels, deriving the DGLAP kernel from algebraic all-order formulas.

Findings

Resummation of off-diagonal channels achieved at leading logarithmic order.

Derived DGLAP kernel series involving Bernoulli numbers.

Identified two-scale nature of off-diagonal splitting functions and Sudakov logs.

Abstract

The off-diagonal parton-scattering channels $g+\gamma^*$ and $q+\phi^*$ in deep-inelastic scattering are power-suppressed near threshold $x\to 1$. We address the next-to-leading power (NLP) resummation of large double logarithms of $1-x$ to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing $d$-dimensional consistency relations from requiring $1/\epsilon$ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large-$x$ limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.