Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
arXiv:1006.0643 · doi:10.1103/PhysRevD.82.034030 10.1103/PhysRevD.82.119907
Abstract
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.
27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56). Results unchanged
References in corpus (11)
- Heavy Quark Masses from Sum Rules in Four-Loop Approximation
- High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
- Reconstruction of heavy quark current correlators at O(α_s^3)
- Charm and Bottom Quark Masses from Perturbative QCD
- Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
- Low energy moments of heavy quark current correlators at four loops
- The second physical moment of the heavy quark vector correlator at O(alpha_s^3)
- Higher Moments of Heavy Quark Correlators in the Low Energy Limit at O(alpha_s^2)
- Muon Anomaly from Lepton Vacuum Polarization and The Mellin--Barnes Representation
- Four-Loop Tadpoles: Applications in QCD
- Precise Charm- and Bottom-Quark Masses: Recent Updates