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

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.

Photon structure functions with heavy particle mass effects

“…The theoretical prediction (red curve) with the charm quark mass effects shows the trend of reducing the massless QCD calculation (purple curve) and becomes consistent with the experimental data. Also shown is the theoretical curve (blue curve) with the resummation prescription given in [12].…”

“…F γ eff to NLO in QCD with charm quark mass effects compared to PLUTO data for n f = 4, Q 2 = 5GeV 2 , P 2 = 0.35GeV 2 , m c = 1.3GeV[12] …”

Photon Structure in Supersymmetric QCD

“…Many authors have studied heavy quark mass effects in the nucleon [12] and the photon structure functions [13,14]. Now we consider the heavy parton mass effects, and we decompose the parton distributions in the case where we have n f − 1 light quarks and one heavy quark flavor which we take the n f -th quark and all the squarks have the same heavy mass, while the gluino has another heavy mass [9,10]:…”

“…Ross and Weston investigated the evolution and threshold effects for the virtual photon structure functions [4]. In this paper based on the framework of treating heavy parton distributions [9,10] we reexamine the effects of the squarks and gluinos appearing in SUSY QCD (SQCD) on the photon structure functions to the leading order in SQCD which can be measured in the two-photon processes of e + e − collision illustrated in Fig.1.…”

Photon structure function in supersymmetric QCD revisited

“…Now we take into account the heavy mass effects by setting the initial conditions for the heavy parton distribution functions as discussed in [18,27,28]. We note here that the structure function F γ 2 can be written as a convolution of the parton distribution q γ (x, Q 2 , P 2 ) and the Wilson coefficient function C(x, Q 2 ):…”