Lattice renormalisation of O(a) improved heavy-light operators: an addendum

TL;DR

This paper provides analytical expressions and numerical values for renormalisation constants of static-light currents at one-loop order, aiding precise calculations of B-meson decay constants in lattice QCD.

Contribution

It offers the first detailed one-loop perturbative renormalisation constants for static-light operators with HYP-smeared static quarks and Wilson light quarks, completing previous work.

Findings

Renormalisation constants computed at one-loop order.

Numerical values provided for static-light currents.

Supports precise lattice QCD calculations of decay constants.

Abstract

The analytical expressions and the numerical values of the renormalisation constants of dimension 3 static-light currents are given at one-loop order of perturbation theory in the framework of Heavy Quark Effective Theory and with an improved gauge action: the static quark is described by the HYP-smeared action and the light quark is of Wilson kind. This completes a work started few years ago and is actually an intermediate step in the measurement of the decay constants $f_{B}$ and $f_{B_{s}}$ by the European Twisted Mass Collaboration [arXiv:1107.1441[hep-lat]].