Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules(17)

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

less contributions in c n from the non-perturbative region.For large n,the subtraction is a exceedingly slow-varying function of Q2.In fact,de?ning y=Λ2/Q2,I?nd at n=20,

y2Fn[...]/(3Q2)

0.12.5761951×1019

0.012.5761877×1019

0.0012.5755872×1019(21) Comparing with the result from Eq.(8),the subtraction is accurate up to one part per million for y=0.1.As n→∞,the large perturbative contributions to C2pert are entirely subtracted,independent of Q2andΛ2.

V.TWIST-FOUR CONTRIBUTION IN POINT-SPLITTING REGULARIZATION The cut-o?scheme discussed in the previous section best illustrates the goal of the OPE: separating the perturbative and soft(infrared)contributions in a process.In analogy with the factorization of the collinear singularities at each twist,the twist separation is not unique. In the cut-o?scheme,this is shown by dependence of higher-twist operators on the cut-o?scaleΛ.The size ofΛmust be large enough so that all non-perturbative physics is covered by higher-twist matrix elements,and at the same time shall be small enough that the pure perturbative physics is included in the coe?cient functions of the leading-twist terms.In QCD,one believes that such scale exists around1GeV2.

In view of what twist-expansion accomplishes,I argue that there exists a large degree of arbitrariness in choosing a cut-o?version of the twist-four operator O4µ:The speci?c cut-o?scheme that I discussed before is only one example.As long as it fully incorporates the non-perturbative physics,as long as it approaches O4µwhen cut-o?is let go to in?nity, any?nite,non-local operator with right dimension and quantum numbers is a good twist-four operator.Once a choice is made,the coe?cient function of the twist-two term can be calculated through applying the OPE to,say,a perturbative zero-momentum quark state. Thus the computation of the coe?cient functions goes hand in hand with the choices of the higher-twist operators.