Mass corrections to the DGLAP equations

TL;DR

This paper introduces a mass-dependent renormalization scheme for the DGLAP equations that naturally incorporates mass effects and decoupling, providing a regulator-free approach based on dispersion relations.

Contribution

It presents a novel mass-dependent MOM scheme for UV renormalization of PDFs that yields mass-dependent splitting functions and respects symmetries without additional regulators.

Findings

Mass-dependent splitting functions are derived for DGLAP equations.

The scheme automatically enforces decoupling and symmetries.

No additional regulators are needed in the renormalization process.

Abstract

We propose a mass-dependent MOM scheme to renormalize UV divergence of unpolarized PDFs at one-loop order. This approach which is based on a once subtracted dispersion relation does not need any regulator. The overall counterterms are obtained from the imaginary part of large transverse momentum region in loop integrals. The mass-dependent characteristic of the scheme yields to mass-dependent splitting functions for the DGLAP evolution equations. While the flavor number is fixed at any renormalization scale, the decoupling theorem is automatically imposed by the mass-dependent splitting functions. The required symmetries are also automatically respected by our prescription.