$B \to π$, $B_{(s)} \to D_{(s)}$ from 2+1+1 Flavor Lattice QCD

Abstract

We present a lattice-QCD calculation of the hadronic form factors for $B$-meson semileptonic decays computed using the highly improved staggered quark action for both valence and sea quarks on the MILC collaborations 2+1+1-flavor ensembles with lattice spacing ranging from 0.09 fm to 0.03 fm, many with physical pion masses On our finest ensembles, we compute the form factors directly at the physical $b$-quark mass. We discuss the computational setup and analysis strategies for two- and three-point correlation functions. For $B_{(s)} \to D_{(s)}$ we present preliminary results of chiral-continuum fits for the scalar and vector form factors. The goal of this project is a percent-level determination of the scalar and vector form factors to enable high-precision determinations of $|V_{ub}|$ and $|V_{cb}|$. This work fits into a broader program of lattice-QCD studies of weak $B$-meson decays by the Fermilab Lattice and MILC Collaborations.

Figures (12)

• Figure 1: Left: Summary of tensions between inclusive and exclusive determinations of $|V_{\rm cb}|$ and $|V_{\rm ub}|$, reproduced from FlavourLatticeAveragingGroupFLAG:2024oxs. A primary goal of the present work is to reduce the theoretical uncertainty for the exclusive decays $B\to\pi\ell\nu$ and $B_{(s)}\to D_{(s)}\ell \nu$ to the roughly $1\%$ level, in line with near-term experimental goals. Right: Global-fit results from the CKMfitter group Charles:2004jd highlighting constraints on the parameters $\alpha,\beta,\gamma$ of the CKM triangle. The parameter $\alpha$ associated with the apex of the CKM triangle is proportional to the ratio $|V_{\rm ub}|/|V_{\rm cb}|$.
• Figure 2: Summary of lattice spacings and light quark masses used in all decay channels. The area of the circles correspond to the number of configurations in the ensemble
• Figure 3: $B$-meson two-point functions on the physical-mass $a\approx0.04 \,\rm{fm}$ ensemble. Left: The correlation functions, excluding data with a noise-to-signal ratio exceeding $30\%$ that are not used in fits. The colors correspond to different heavy quark masses. Right: Effective masses for each correlator plotted separately on even and odd time sliices (denoted with triangles or circles), in approximate physical units. Although noise increases with heavy quark mass, a large plateau region in Euclidean time is observed for all correlators. Note that that the largest heavy quark mass on this ensemble corresponds to a meson mass $M_B \approx 5.3 \,\rm{GeV}$.
• Figure 4: Fit posteriors for the ground-state $B$-meson energy with $am_h \approx am_b$ on the physical-mass ensemble with $a\approx 0.04 \, \rm{fm}$. The color indicates the number of states included in the fit to the truncated spectral decomposition. The $x$-axis indicates the starting time of the fit. For data points with the same color (i.e. set number of states), the posteriors can be seen to reach a plateau value as $t_{\rm min}\xspace$ is increased before the signal eventually begins to degrade. As more states are included in the fit, stable extractions of the ground-state mass become possible at earlier Euclidean times.
• Figure 5: Ratio of two-point and three-point functions for different momenta, compared to fit posteriors for the bare form factors, at $a m_h \approx am_b$ on the physical-mass $a\approx 0.04$ fm ensemble for $B\to\pi$. The right panel shows the form factors as a function of the squared momentum of the pion, where $\bm{p}^2 = (2\pi/L)^2 \bm{n}^2$ with $\bm{n} \in \mathbb{Z}^3$.