Beauty Physics in Lattice Gauge Theory

TL;DR

This paper reviews lattice gauge theory calculations of leptonic decay constants for D and B mesons, analyzing systematic errors, comparing results from different groups, and discussing implications for understanding heavy-light meson properties.

Contribution

It provides a systematic comparison of lattice QCD results for decay constants and estimates their values in the quenched approximation, highlighting sources of uncertainties and future improvements.

Findings

Estimated decay constants $f_D$ and $f_B$ with systematic errors.

Comparison between quenched and full QCD results.

Discussion of related quantities like $B$-parameters and hadron spectra.

Abstract

We summarize the present status of lattice gauge theory computations of the leptonic decay constants $f_D$ and $f_B$. The various sources of systematic errors are explained in a manner easily understood by the non--expert. The results obtained by the different groups are then systematically compared. As a result, we derive estimates for $f_D$ and $f_B$ in the quenched approximation through an appropriate combination of the data available from the different groups. Since we account for a possible lattice spacing dependence, the final errors are quite large. However, it is now well known how these uncertainties can be reduced. For the decay constant of heavy--light pseudoscalar mesons with masses of 1-2~GeV, an interesting comparison of a full QCD result with the corresponding simulation in the quenched approximation can be done. Effects of sea quarks of mass $m_s$ are below the statistical accuracy of these simulations. Related quantities, like $B$--parameters, the spectrum of beauty--hadrons and the breaking of the QCD string are discussed briefly.