Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules(2)

Infrared renormalons and $1/Q^2$ power corrections in deep-inelastic sum rules are studied. The renormalization of operators with power divergence are discussed. The higher-twist terms in the operator product expansion are shown to account for the residual

I.INTRODUCTION

Deep-inelastic sum rules—Bjorken sum rule[1],Gross-Llewellyn Smith sum rule[2], Ellis-Ja?e sum rule[3],and a whole zoo of similar sum rules[4]—are fascinating things to study,both from theoretical and experimental points of view.These sum rules form one of the clearest tests of perturbative and non-perturbative Quantum Chromodynamics(QCD), and tests of our ability to solve the theory as well.Some of the sum rules were derived before QCD was advanted,in current algebras that the asymptotic QCD turns out to respect up to logarithms.In QCD,they can be derived using the technique of Wilson’s operator product expansion(OPE)or its equivalent.The imprints of QCD in these sum rules are radiative corrections,which can be calculated perturbatively,and the higher-twist corrections that involve high-dimensional hadron matrix elements.This paper is intended to address the issue on the separation of these two e?ects and some related aspects in the OPE.

In order to be speci?c,I will center my discussion on the Bjorken sum rule,which presently is under active experimental study[5].The sum rule is for the nucleon’s spin-dependent structure function g1(x,Q2)and the QCD version reads[6],

10(g p1(x,Q2)?g n1(x,Q2))dx=127C4(αs(Q2)) Oµ4

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