Exclusive semileptonic $B \to π\ell ν_\ell$ and $B_s \to K \ell ν_\ell$ decays through unitarity and lattice QCD

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V ub | is obtained from exclusive semileptonic B → π ν and B s → K ν 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 |V ub | from the experimental data, obtaining |V ub | = (3.62±0.47)•10 −3 from B → π and |V ub | = (3.81±1.03)•10 −3 from B s → K. These results are compatible with the most recent inclusive value |V ub | incl = 4.13 (26) • 10 −3at the 1σ level. We also present purely theoretical estimates of the ratio of the τ /µ differential decay rates R τ /µ π(K) , the normalized forward-backward asymmetry Ā ,π(K) F B and the normalized lepton polarization asymmetry Ā ,π(K) polar .

LFU ratios in B decays using Lattice QCD and Unitarity

“…The DM results are shown in Table I for each LQCD input. The combined case in the last column corresponds to the combination of the RBC/UKQCD and the FNAL/MILC data, as described in [21]. They are all compatible with the only available measurement by Belle [24] R τ /µ π | exp = 1.05 ± 0.51, (20) which has a large uncertainty compared to theoretical predictions.…”

“…Let us discuss, for instance, the case of the B → π ν decays [21]. They are characterized by two FFs, which are analogous to the ones defined in Eq.…”

A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

“…A common approach in the literature has been to focus on the high-q 2 behavior and then extend the calculation to full kinematic range using the z-expansion [123][124][125][126]. Recent work has revived old ideas about using dispersive bounds [127][128][129][130][131] to constrain the low-q 2 behavior of the form factors given results at high q 2 . Even though covering the full q 2 range is computationally challenging, comparing the shape of the form factors to the experimental data across q 2 provides further insight on the quality of our theoretical description of the experimental process.…”

Exclusive B-meson semileptonic decays from unitarity and lattice QCD

“…In Ref. [17] the DM method has been applied to the study of the 𝐵 → 𝜋ℓ𝜈 ℓ decays by evaluating the relevant susceptibilities from suitable two-point correlation functions ad adopting for the hadronic FFs the lattice results of RBC/UKQCD [18] and FNAL/MILC [19] Collaborations at large values of the 4-momentum transfer.…”