Resummation of large logarithms in the heavy quark effects on the parton distributions inside the virtual photon

TL;DR

This paper develops a method to resum large logarithmic terms caused by heavy quark masses in the parton distribution functions of the virtual photon, improving theoretical predictions.

Contribution

It introduces a new resummation technique incorporating heavy quark mass effects into the DGLAP evolution equations for virtual photon parton distributions.

Findings

Successfully resummed large logarithmic terms due to heavy quark masses.

Reproduced known NLO heavy quark effects in a specific kinematic limit.

Numerical calculations show the impact of resummation on parton distributions.

Abstract

We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and discuss the property of the resummed heavy quark effects.