Heavy Flavor Contributions to QCD Sum Rules and the Running Coupling Constant

TL;DR

This paper calculates heavy flavor corrections to QCD sum rules in deep inelastic scattering, compares them with massless quark series, and discusses implications for the running coupling constant and its extrapolation to high energies.

Contribution

It introduces first and second order heavy flavor corrections to sum rules and proposes an alternative description of the running coupling in the MOM-scheme.

Findings

Large logarithms dominate at higher Q^2/m^2 ratios.

Matching conditions are insufficient for extrapolating ppa_s to M_Z scale.

An alternative MOM-scheme description is suggested.

Abstract

We have calculated first and second order corrections to several sum rules measured in deep inelastic lepton-hadron scattering. These corrections, which are due to heavy flavors only, are compared with the existing perturbation series which is computed for massless quarks up to third order in the strong coupling constant \alpha_s. A study of the perturbation series reveals that the large logarithms of the type ln^i Q^2/m^2 dominate the perturbation series at much larger values than those given by the usual matching conditions imposed on the \alpha_s(\mu). Therefore these matching conditions cannot be used to extrapolate the running coupling constant from small \mu to very large scales like \mu=M_Z. An alternative description of the running coupling constant in the MOM-scheme is proposed.