Heavy Quark Effects in the Virtual Photon Structure Functions

Abstract

We investigate the heavy quark mass effects in the virtual photon structure functions $F_{2}^{\gamma}(x, Q^2, P^2)$ and $F_{L}^{\gamma}(x, Q^2, P^2)$ in the framework of the mass-independent renormalization group equation (RGE). We study a formalism in which the heavy quark mass effects are treated based on parton picture as well as on the operator product expansion (OPE), and perform the numerical evaluation of $F_{\rm eff}^{\gamma}(x, Q^2, P^2)$ to the next-leading order (NLO) in QCD.Comment: 19 pages, LaTeX, 4 eps figures, PTPTe

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.…”

Top quark effects on the virtual photon structure function at ILC

“…We use the formalism in Ref. [28] for the calculation of photon structure functions by OPE and we use the results in Ref. [24] by QPM.…”

“…In the formalism of Ref. [28], it is assumed that we divide the n f quarks system into two parts, namely n f − 1 massless quarks system and one massive quark. We apply this formalism to the virtual photon structure functions at the ILC and we assume that u, d, s, c, b are massless quarks and t is the massive quark at the kinematical region expected at the ILC.…”

“…where the expression of the coefficients ∆A n i , ∆B n i and ∆C n are given in Ref. [28] and all finite coefficients are related with the variation of the operator matrix element for the top quark due to mass effects. The variation by the heavy quark effects to coefficients in M γ L is zero up to this order.…”