Challenging $\bar{B}_{(s)}\to D_{(s)}^{(*)}$ Form Factors with the Heavy Quark Expansion

TL;DR

This paper analyzes recent lattice QCD predictions for B to D form factors within the heavy-quark expansion framework, introducing unitarity bounds and providing new predictions for decay observables.

Contribution

It is the first to impose unitarity bounds on all B to D form factors, including tensor form factors, within the HQE framework and to compare lattice results with sum rule estimates.

Findings

Lattice QCD results are compatible within the HQE fit.

Tensor form factor bounds are currently not constraining the parameter space.

Predictions for angular observables and LFU ratios are provided.

Abstract

Recent publications by three lattice QCD collaborations have provided an unprecedented wealth of theoretical predictions for the $\bar{B}_q \to D_q^{(*)}$ form factors, for spectator flavours $q=u/d$ and $q=s$. We analyse these predictions within the framework of the heavy-quark expansion (HQE) to order $\alpha_s$, $1/m_b$, and $1/m_c^2$. For the first time, our analysis imposes unitarity bounds for all of the $\bar{B}_q^{(*)} \to D_q^{(*)}$ form factors; this includes newly identified tensor form factors arising in $\bar{B}_q^*\to D_q^{(*)}$. This enables us to treat all form factors in the same fashion. At the level of our present analysis, the inclusion of the tensor bounds is not yet constraining the HQE parameter space. We find the lattice QCD results to be well compatible with each other in a joint HQE fit as well as with QCD sum rule estimates that were used in previous HQE analyses. This is in contrast to the strong variability of the posterior predictions, in particular of the form factors ratios $R_0$ and $R_2$. Using the posterior distributions of our HQE analysis, we provide predictions for angular observables and LFU ratios in the $\bar{B}_q \to D_q^{(*)}\ell^-\bar{\nu}$ decays.