Untangling the heavy-flavor mess: status of the Fermilab-MILC calculation of the $B_{(s)}\to D^{(\ast)}_{(s)}\ell\nu$ form factors

TL;DR

This paper reports on the status of lattice QCD calculations of $B_{(s)} o D^{( ext{ast})}_{(s)}\,\ell\nu$ form factors, highlighting recent progress and ongoing challenges in understanding heavy-flavor decays.

Contribution

It provides updated lattice QCD results for heavy-to-heavy and heavy-to-light decay form factors using multiple ensembles, addressing discrepancies and unresolved tensions.

Findings

Form factors calculated on 7 ensembles with physical pion masses.

Recent advances have not clarified the inclusive vs exclusive decay puzzle.

Lattice results for $B\to D^{\ast}\ell\nu$ form factors remain unclear.

Abstract

We present the status of calculations of the form factors of the most relevant heavy-to-heavy and heavy-to-light decay channels. Using seven $N_f = 2+1+1$ HISQ ensembles, with lattice spacings ranging from 0.15 fm down to 0.06 fm, we calculate the form factors of the decays, including correlations among them. More than half of our ensembles feature physical pion masses, and the heavy quarks are simulated at their physical masses using the Wilson-clover action with the Fermilab interpretation. Even though we have recently seen huge qualitative and quantitative leaps in the characterization of heavy-to-heavy decays, these advances have failed to translate into improvements for the inclusive vs exclusive question, or the matter of the Lepton Flavor Universality ratios. In particular, in the $B\to D^{\ast}\ell\nu$ channel, the current situation of the lattice-QCD form factors is far from clear. Further, the latest lattice-QCD results on the heavy-to-light form factors display unexplained tensions that must urgently be resolved. The work presented here is an attempt to address these issues.