Eur. Phys. J. C 70, 999-1007 (2010)
https://doi.org/10.1140/epjc/s10052-010-1494-0

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

¹ Department of Physical Science, Faculty of Science, Hiroshima University, Higashi, Hiroshima, 739-8526, Japan
² KEK Theory Centre, Tsukuba, Japan
³ Department of Physics, Graduate School of Science, Kyoto University, Yoshida, Kyoto, 606-8501, Japan
⁴ Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

uematsu@scphys.kyoto-u.ac.jp

Received: 3 August 2010
Revised: 8 October 2010
Published online: 16 November 2010

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 we discuss the property of the resummed heavy-quark effects.