Chebyshev and Backus-Gilbert reconstruction for inclusive semileptonic $B_{(s)}$-meson decays from Lattice QCD

TL;DR

This paper compares Chebyshev and Backus-Gilbert methods for nonperturbative lattice QCD calculations of inclusive semileptonic B-meson decays, aiming to improve CKM matrix element determinations.

Contribution

It introduces and compares two analysis techniques for lattice QCD data on B-meson decays, providing insights into their effectiveness and differences.

Findings

Both methods successfully analyze lattice data for B_s decays.

The study highlights the strengths and limitations of each approach.

Results contribute to resolving CKM matrix element discrepancies.

Abstract

We present a study on the nonperturbative calculation of observables for inclusive semileptonic decays of $B_{(s)}$ mesons using lattice QCD. We focus on the comparison of two different methods to analyse the lattice data of Euclidean correlation functions, specifically Chebyshev and Backus-Gilbert approaches. This type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$. We report the results from a pilot lattice computation for the decay $B_s \rightarrow X_c \, l\nu_l$, where the valence quark masses are approximately tuned to their physical values using the relativistic-heavy quark action for the $b$ quark and the domain-wall formalism for the other valence quarks. We address the computation of the total decay rate as well as leptonic and hadronic moments, discussing similarities and differences between the two analysis techniques.