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

Jun, 2010
27 pages
Published in:
  • Phys.Rev.D 82 (2010) 034030,
  • Phys.Rev.D 82 (2010) 119907 (erratum)
e-Print:

Citations per year

201020132016201920220123456
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