Operator product expansion in static-quark effective field theory: large perturbative correction

TL;DR

This paper computes operator product expansion coefficients in static-quark effective field theory, revealing large perturbative corrections that challenge the reliability of certain sum rule-based decay constant determinations.

Contribution

It provides exact two-loop calculations of operator coefficients up to dimension 7 in a general gauge and spacetime dimension, extending previous results and highlighting significant perturbative effects.

Findings

Two-loop coefficients for d<=7 operators calculated

Perturbative corrections can reach 100%, affecting decay constant estimates

Results applicable to arbitrary gauge groups and dimensions

Abstract

We calculate the coefficients of operators with dimensions d <= 7 in the operator product expansion of correlators of q Gamma Q currents, for the effective field theory of an infinite-mass quark, Q. Exact two-loop results are obtained, with an arbitrary gauge group and spacetime dimension, for the perturbative (d=0) and quark-condensate (d=3) contributions, confirming our previous result for the anomalous dimension of the current. Leading-order results are given for light-quark operators with d=5, 6, 7 and gluon operators with d=4, 6. The existence of a perturbative correction of order 100% precludes a reliable determination of f_B from non-relativistic sum rules.