Form factors of $B\toπ\ellν$ and a determination of $|V_{ub}|$ with Möbius domain-wall-fermions

Abstract

Using a fully relativistic lattice fermion action, we compute the form factors of the semileptonic decay B → π ν, which is required for the determination of the Cabibbo-Kobayashi-Maskawa matrix element |V ub |. We employ the Möbius domain-wall fermion formalism for the generation of lattice ensembles with 2+1 sea quark flavours as well as for the valence heavy and light quarks. We compute the form factors at various values of the lattice spacing and multiple light and heavy quark masses, and extrapolate the results to the physical point. We combine our lattice results with the available experimental data to obtain |V ub | = (3.93 ± 0.41) × 10 −3 .

Heavy flavor physics from lattice QCD

“…The best precision of ≈ 4 % has been achieved by Fermilab/MILC by simulating the lattice cutoffs ≲ 4.4 GeV, pion masses down to 𝑀 𝜋 ∼ 165 MeV and by using the so-called Fermilab approach, namely a HQET re-interpretation of the Wilson quark action [10]. Recently, the JLQCD Collaboration calculated the form factors through the relativistic approach using the Möbius domain-wall action [11] for all relevant quark flavors [9]. Their accuracy is typically 10 % at similar lattice cutoffs but with larger 𝑀 𝜋 ≳ 230 MeV.…”

“…𝑠 ℓ𝜈 exclusive decay (dased lines). All data are calculated on a JLQCD ensemble at 𝑎 −1 ≈ 3.6 GeV and 𝑀 𝜋 ≈ 300 MeV [9]. Right: comparison of X𝐿,𝜎→0 (q 2 ) with conventional OPE calculation.…”

Lattice QCD study of inclusive semileptonic decays of heavy mesons

“…See the supplementary materials of ref. [22] for details of the gauge configurations. It employs Möbius domain-wall fermions for both valence and sea quarks.…”

Relativistic description of the semileptonic decays of bottom mesons

“…From this plot we see that the form factor f + (q 2 ) in RQM rapidly grows for q 2 > 15 GeV 2 up to the value f + (q 2 max ) = 10.9 , while this form factor in CLFQM reaches only the value f + (q 2 max ) = 1.27 which is almost an order of magnitude lower. In the same figure we also give lattice QCD results [27][28][29][30][31][32] which are available in the high q 2 > 15 GeV 2 region. The form factors of the B s → K semileptonic transitions in RQM and CLFQM in comparison with lattice QCD data [30,[32][33][34] are plotted in Fig.…”

“…Such comparison provides the test of the lepton universality and deviations of the standard model predictions from experimental data can indicate the possible ) and the lower ones to f 0 (q 2 ). Lattice results are plotted: HPQCD [27] by triangles (blue f + (q 2 ), green f 0 (q 2 )) with error bars, FNAL/MILC [28,29] by squares (red f + (q 2 ), magenta f 0 (q 2 )) with error bars, RBC/UKQCD [30] by filled circles (cyan f + (q 2 ), orange f 0 (q 2 )) with error bars, and JLQCD [31] by diamonds (purple f + (q 2 ), yellow f 0 (q 2 )) .…”