Position-space renormalization schemes for four-quark operators in HQET

TL;DR

This paper develops position-space renormalization schemes for four-quark operators in HQET, enabling nonperturbative renormalization in lattice QCD and providing O(α_S) matching coefficients for heavy-hadron phenomenology.

Contribution

It introduces X-space schemes for HQET operators and computes their one-loop matching coefficients to connect lattice results with continuum MSbar schemes.

Findings

Derived O(α_S) matching coefficients for HQET four-quark operators.

Demonstrated nonperturbative cancellation of power divergences in static-quark self-energy.

Provided tools for precise lattice QCD calculations of heavy-hadron properties.

Abstract

X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MSbar in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MSbar-renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O($\alpha_S$) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B-Bbar mixing.