Mass corrections to the DGLAP equations

A Jamali Hafshejani,A Mirjalili

doi:10.1103/physrevd.103.054026

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.

Highlights

The Wilson operator product expansion (OPE) [1,2] provides a systematic approach to the factorization of quantum chromodynamics (QCD) [3,4], namely, the separation of contributions from long and short distances
The universal parton distribution functions (PDFs) are factorized from the hard partonic scattering. The latter can be calculated within perturbative QCD, but the PDFs have to be determined in a global analysis using experimental data [5,6] and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations [7,8,9] that provide the scale evolution of the PDFs
We subtract large transverse momenta behavior of bare PDFs, which belong to the hard region

Summary

INTRODUCTION

The Wilson operator product expansion (OPE) [1,2] provides a systematic approach to the factorization of quantum chromodynamics (QCD) [3,4], namely, the separation of contributions from long and short distances. The MOM characteristic of our scheme implies that the decoupling theorem is imposed automatically and smoothly by mass correction terms in the splitting functions, while the flavor number is fixed. This scheme yields the following computational simplifications: One only uses finite cut diagrams in a large transverse momenta region (full evaluation is not needed).

DEFINITIONS

OUR PROPOSED RENORMALIZATION SCHEME

MASS-DEPENDENT SPLITTING FUNCTIONS

CONCLUSION