Study on the systematic effects on $b \to c$ inclusive semileptonic decays

TL;DR

This paper explores lattice QCD calculations of inclusive semileptonic $B_s$ decays to address the $|V_{cb}|$ tension, focusing on systematic uncertainties and innovative reconstruction techniques.

Contribution

It introduces a method to isolate excited-state contributions in inclusive decay rate calculations, reducing systematic uncertainties.

Findings

Chebyshev reconstruction results demonstrate potential for precise decay rate computation.

Systematic uncertainties from source-sink smearing and separation are analyzed and mitigated.

Exclusive decay treatment of ground states improves the accuracy of inclusive decay estimates.

Abstract

We discuss the calculation of the inclusive semileptonic decay for the process $B_s \to X_c \, l \nu_l$ using lattice QCD. This calculation could be decisive in understanding the long-standing tension between inclusive and exclusive determinations of the CKM matrix element, $|V_{cb}|$. In this talk, we investigate the main sources of systematic uncertainty in these decays, including the impact of Jacobi smearing at the source and sink, variations in source-sink separation, and the intrinsic uncertainties of the inclusive reconstruction method itself. In addition, we explain how we can restrict the reconstruction of the inclusive decay rate to just the excited-state contributions. This is achieved by treating the ground-state contributions as an exclusive decay with well-controlled conventional techniques. Systematic effects from the reconstruction then only affect excited-state contributions. Where these are sub-dominant, a suppression of systematic effects is expected. We show results based on Chebyshev reconstruction, which are part of a larger effort towards a first phenomenologically relevant computation of the inclusive decay rate in the continuum and infinite-volume limits.