Spin structure function of the virtual photon beyond the leading order in QCD

Abstract

Polarized photon structure can be studied in the future polarized e + e − colliding-beam experiments. We investigate the spin-dependent structure function of the virtual photon g γ 1 (x, Q 2 , P 2 ), in perturbative QCD for Λ 2 ≪ P 2 ≪ Q 2 , where −Q 2 (−P 2 ) is the mass squared of the probe (target) photon. The analysis is performed to next-to-leading order in QCD. We particularly emphasize the renormalization scheme independence of the result.The non-leading corrections significantly modify the leading log result, in particular, at large x as well as at small x. We also discuss the non-vanishing first moment sum rule of g γ 1 , where O(α s ) corrections are computed.

ααs2corrections to the first moment of the polarized virtual photon structure functiong1γ(x,Q

“…In the case of a virtual photon target (P 2 = 0) there appear two spin-dependent structure functions, g γ 1 (x, Q 2 , P 2 ) and g γ 2 (x, Q 2 , P 2 ). The former has been investigated up to the NLO by the present authors in [14,15], and also in the second paper of [13]. In Refs.…”

“…[14] to obtain the NLO (αα s ) corrections to the sum rule shown in Eq.(1.3). On the other hand, A (2) S is nonvanishing and will be calculated in Sec.…”

“…In fact, for the case Λ 2 ≪ P 2 ≪ Q 2 , the first moment has been calculated up to the NLO (αα s ), as follows [8,14];…”

“…In Refs. [14,15] the structure function g γ 1 (x, Q 2 , P 2 ) was analyzed in the kinematical region…”

Virtual photon structure functions

“…Here we note the relation between the 8 structure functions (4) and the 8 helicity amplitudes (9), which are given by…”