arXiv 1006.06432010-06hep-phhep-lathep-thmath-phmath.MP

重夸克关联函数的阈展开、低能展开和高能展开的恢复

Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators

D. Greynat, S. Peris

备注：: 27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56). Results unchanged
发表信息：: Phys.Rev.D82:034030,2010; Erratum-ibid.D82:119907,2010
DOI：: 10.1103/PhysRevD.82.034030 10.1103/PhysRevD.82.119907

摘要：

利用Mellin-Barnes变换，我们给出了如何系统地同时对重夸克相关子在q^2=0（低能）、q^2= 4 m^2（阈值，其中m是夸克质量）和q^2=- \infty（高能）附近的展开求和.我们在O（alpha_s^2）和O（alpha_s^3）的情况下证明了微扰矢量相关器的方法。我们证明了真空极化函数的泰勒展开式的系数Ω（n），对于大的n，可以用1/n的幂展开式（直到n的1/2次方）来精确计算。这个大n展开式有一个由OPE的矩给出的符号交替分量，和一个由外动量q^2中的阈值展开式的矩给出的符号固定分量。

英文摘要：

With the help of the Mellin-Barnes transform, we show how to simultaneously resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2= 4 m^2 (threshold, where m is the quark mass) and q^2=-\infty (high-energy) in a systematic way. We exemplify the method for the perturbative vector correlator at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of the Taylor expansion of the vacuum polarization function in terms of the conformal variable ωadmit, for large n, an expansion in powers of 1/n (up to logarithms of n) that we can calculate exactly. This large-n expansion has a sign-alternating component given by the logarithms of the OPE, and a fixed-sign component given by the logarithms of the threshold expansion in the external momentum q^2.

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