Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules(11)

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

no logarithmic divergence at all but still is cut-o?dependent.One important consequence of this is that there are no physically well-de?ned higher-twist contributions in the OPE.

Since the physical quantity that is expanded in the OPE is well-de?ned,the ambiguity in de?ning higher-twist operators must be correlated with the infrared renormalon singularities in the coe?cient functions.In the2D non-linear sigma model,David showed that the di?erent choices for regularizing the Borel integral and de?ning the composite operators give the same?nal result.Thus despite the existence of arbitrariness in de?ning the contributions of di?erent twists,the spirit of OPE is unspoiled.

In fact,the situation with the twist separation is analogous to the factorization of collinear singularities in the OPE[18].There the leading-twist contribution in the OPE can be written as a product of the coe?cient functions and the hadron matrix elements. The coe?cient functions depend on the factorization scale because they are obtained by subtracting o?collinear divergence in a single parton scattering.The matrix elements are scale-dependent because the local operators are renormalized operators disposed of ultra-violet divergence.The factorization scale controls how much physics is considered to be perturbative and how much is non-perturbative.Their product is scale-independent.

IV.OPERATOR PRODUCT EXPANSION IN A CUT-OFF SCHEME According to the previous two sections,the traditional recipe for the OPE is at best formal:The coe?cient functions are intrinsically divergent and higher-twist operators are ill-de?ned after removing the logarithmic divergence.However,both problems have a common origin—the IR renormalons.The existence of the renormalons makes the notion of twist separation procedure-dependent,however,speci?cs cancel in the physical sum.Speci?cally, one needs to de?ne the limit?→0in higher-twist operators consistent with handling of the Borel integral for the coe?cient functions[15].However,the approach is hardly useful in practical applications.First,no one knows how to calculate the non-perturbative matrix elements of higher-twist operators in dimensional regularization in QCD.Second, despite tremendous progress made recently in calculating the QCD perturbative series to higher orders[19],it remains a formidable task to calculate the exact behavior of a infrared renormalon stly,even all the above are possible,the regularization does not seem to have clear physical motivation.[The author noticed a number of other proposals in the literature for regularization the infrared renormalons[12,23].]

To my opinion,a better approach to the OPE,which was advocated by the former ITEP group[24,25],and was?rst taken seriously by Mueller[16],is to consider the twist expansion entirely from the point of view of Feynman diagrams.Imagine a set of Feynman diagrams completely de?ne a physical cross section or a correlation function in QCD.Often in accompany with a high-energy subdiagram,there are soft subprocesses mediated by low-energy quarks and gluons,which result in soft(infrared)and collinear(mass)divergence in perturbative calculations[18].In many physical observables,the soft divergence cancel according to equivalent of the Kinoshita-Lee-Nauenburg theorem[26],and the collinear divergence can be factorized into hadron matrix elements,which in the end are replaced with proper non-perturbative ones[11].The remaining part is calculable as a perturbation series in the strong coupling constantαs and is called infrared safe.The classical examples of the perturbative-calculable quantities include the total rate for e+e?→hadron,the coe?cients

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新高等教育Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules(11)全文阅读和word下载服务。