Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
Jun, 201027 pages
Published in:
- Phys.Rev.D 82 (2010) 034030,
- Phys.Rev.D 82 (2010) 119907 (erratum)
e-Print:
- 1006.0643 [hep-ph]
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Abstract: (arXiv)
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.- 12.38.Aw
- 12.38.Bx
- 12.38.Cy
- threshold: expansion
- correlation function: vector
- resummation: threshold
- Taylor expansion
- heavy quark
- vacuum polarization
- operator product expansion
References(26)
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