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

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

2010-06-03

arxiv.org/abs/1006.0643v2

Phys.Rev.D82:034030,2010; Erratum-ibid.D82:119907,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56). Results unchanged

Scientific paper

10.1103/PhysRevD.82.034030 10.11

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 \omega admit, 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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