Inclusive and exclusive semileptonic decays of heavy mesons on the lattice

TL;DR

This work addresses the persistent tension in $|V_{cb}|$ by pursuing a unified lattice QCD treatment of inclusive and exclusive semileptonic heavy-meson decays via four-point correlators. The main approach combines kernel-based reconstruction for inclusive observables, using a Chebyshev expansion to control omitted higher-order terms, with multi-exponential fits and HQET-guided parameterizations for exclusive form factors, all on RBC/UKQCD ensembles. The results on $B_s\to X_{cs}$ show the simultaneous limits $\sigma \to 0$ and $N \to \infty$ are approaching stability, with $f_+^s$ and $f_0^s$ in agreement with prior HPQCD results within uncertainties, and HQET-based P-wave analysis offering insights into the $1/2$-$3/2$ puzzle. This work lays groundwork for a unified lattice framework to reduce systematic gaps between inclusive and exclusive determinations and guides future improvements in controlling systematics and extending to other decays.

Abstract

We report the recent progress from our group in extracting observables of both inclusive and exclusive semileptonic heavy-meson decays directly from lattice QCD four-point correlators. On the inclusive side, we illustrate how to estimate the systematic uncertainties from omitted higher-order terms and non-zero smearing of the kernel approximation, building on two important features of the Chebyshev expansion. On the exclusive side, we perform BCL parameterizations of the pseudoscalar to pseudoscalar form factors and compare the fitted coefficients with those from earlier results by HPQCD. We also perform a HQET-based parameterization of the P-wave form factors to shed new light on the 1/2-vs-3/2 puzzle. This work constitutes a step toward a unified lattice treatment of inclusive and exclusive semileptonic decays, relevant for the Vcb puzzle. In this study, we use lattice ensembles from the RBC/UKQCD collaboration for numerical investigations. Future developments from our group will focus on the control of other systematic effects for inclusive decays and investigations of other techniques with reduced statistical errors to extract exclusive contributions from lattice four-point correlators.

Figures (2)

• Figure 1: We present the effects of the $N\rightarrow\infty$ and $\sigma\rightarrow 0$ limits, taken simultaneously with $\sigma = 1/N$, on the total $\bar{X}$ of $B_s\rightarrow X_{cs}$ at all simulated momenta.
• Figure 2: The BCL parameterisations (lines) are compared with the lattice data (data points) for pseudoscalar to pseudoscalar form factors for $B_s$ semileptonic decays, i.e., $f_+^s$ and $f_0^s$. Noticing that we have a somewhat different $q^2$ range compared with that in Ref. McLean:2019qcx due to unphysical choices of heavy quark masses in our simulations.