The B-meson mass splitting from non-perturbative quenched lattice QCD

TL;DR

This paper non-perturbatively renormalizes the chromo-magnetic operator in quenched lattice QCD to improve the theoretical prediction of B-meson mass splitting, achieving results closer to experimental data.

Contribution

It provides the first non-perturbative renormalization of the chromo-magnetic operator in quenched lattice QCD and refines the B-meson spin splitting calculation.

Findings

Renormalization factors are computed with negligible uncertainty.

Results align more closely with experimental B-meson mass splitting.

Provides parametrizations of the matching coefficient for practical use.

Abstract

We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.