The Heavy Quark Self-Energy in Nonrelativistic Lattice QCD

TL;DR

This paper calculates the heavy quark self-energy in nonrelativistic lattice QCD to one-loop order, analyzing the effects of tadpole contributions and the effectiveness of tadpole improvement schemes.

Contribution

It provides a detailed perturbative calculation of heavy quark self-energy including relativistic corrections and evaluates tadpole improvement in lattice QCD.

Findings

Large tadpole contributions to renormalization parameters.

Tadpole improvement effectively reduces these large contributions.

Results for mass and wavefunction renormalization are presented.

Abstract

The heavy quark self-energy in nonrelativistic lattice QCD is calculated to $O(\alpha_s)$ in perturbation theory. An action which includes all spin-independent relativistic corrections to order $v^2$, where $v$ is the typical heavy quark velocity, and all spin-dependent corrections to order $v^4$ is used. The standard Wilson action and an improved multi-plaquette action are used for the gluons. Results for the mass renormalization, wavefunction renormalization, and energy shift are given; tadpole contributions are found to be large. A tadpole improvement scheme in which all link variables are rescaled by a mean-field factor is also studied. The effectiveness of this scheme in offsetting the large tadpole contributions to the heavy quark renormalization parameters is demonstrated.