Exclusive semileptonic $B \to \pi \ell \nu_\ell$ and $B_s \to K \ell \nu_\ell$ decays through unitarity and lattice QCD

TL;DR

This paper determines the CKM matrix element |V_ub| from exclusive semileptonic B decays using a unitarity-based approach and lattice QCD, providing results compatible with inclusive measurements and offering theoretical predictions for decay observables.

Contribution

The study introduces a unitarity-based dispersion matrix method combined with lattice QCD to accurately determine form factors and extract |V_ub| without relying on experimental shape assumptions.

Findings

|V_ub| from B→π: (3.62 ± 0.47)×10^{-3}

|V_ub| from B_s→K: (3.77 ± 0.48)×10^{-3}

Average |V_ub|: (3.69 ± 0.34)×10^{-3}

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\vert V_{ub}\vert$ is obtained from exclusive semileptonic $B \to \pi \ell \nu_\ell$ and $B_s \to K \ell \nu_\ell$ decays adopting the unitarity-based dispersion matrix approach for the determination of the hadronic form factors (FFs) in the whole kinematical range. We use lattice computations of the relevant susceptibilities and of the FFs in the large-$q^2$ regime in order to derive their behavior in the low-$q^2$ region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address the extraction of $\vert V_{ub}\vert$ from the experimental data, obtaining $\vert V_{ub}\vert = (3.62 \pm 0.47) \cdot 10^{-3}$ from $B \to \pi$ and $\vert V_{ub}\vert = (3.77 \pm 0.48) \cdot 10^{-3}$ from $B_s \to K$, which after averaging yield $\vert V_{ub}\vert = (3.69 \pm 0.34) \cdot 10^{-3}$. These results are compatible with the most recent inclusive value $\vert V_{ub} \vert_{incl} = 4.13\,(26) \cdot 10^{-3}$ at the 1$\sigma$ level. We also present purely theoretical estimates of the ratio of the $\tau/\mu$ decay rates $R^{\tau/\mu}_{\pi(K)}$, the normalized forward-backward asymmetry $\bar{\mathcal{A}}_{FB}^{\ell,\pi(K)}$ and the normalized lepton polarization asymmetry $\bar{\mathcal{A}}_{polar}^{\ell,\pi(K)}$.