$|{V}_{cb}|$ and $R({D}^{(*)})$ using lattice QCD and unitarity

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$| V_{c b} |$ and $R (D^{(*)})$ using lattice QCD and unitarity

G. Martinelli, S. Simula, and L. Vittorio

Phys. Rev. D 105, 034503 – Published 7 February 2022

Abstract

The Cabibbo-Kobayashi-Maskawa matrix element $| V_{c b} |$ is extracted from exclusive semileptonic $B \to D^{(*)}$ decays adopting a novel unitarity-based approach which allows one to determine in a full nonperturbative way the relevant hadronic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B \to D^{(*)}$ FFs at small recoil from FNAL/MILC and JLQCD Collaborations, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence and without constraining their shape using experimental data. Thus, we address the extraction of $| V_{c b} |$ from the experimental data on the semileptonic $B \to D^{(*)} ℓ ν_{ℓ}$ decays, obtaining $| V_{c b} | = (41.0 \pm 1.2) \times 10^{- 3}$ from $B \to D$ using as input the final FNAL/MILC lattice data for the FFs and $| V_{c b} | = (40.4 \pm 1.8) \times 10^{- 3}$ from $B \to D^{*}$ using the preliminary JLQCD lattice data. Our result from $B \to D$ is consistent within $\sim 1$ standard deviation with the most recent inclusive determination $| V_{c b} |_{incl} = (42.00 \pm 0.65) \times 10^{- 3}$ . The resulting uncertainty is comparable with those obtained in literature using experimental data to constrain the shape of the FFs. Our result from $B \to D^{*}$ , though consistent with $| V_{c b} |_{incl}$ , is still based on preliminary lattice data for the FFs and its uncertainty, is greater than the ones obtained in literature using experimental data to constrain the shape of the FFs. We investigate also the issue of lepton flavor universality thanks to new theoretical estimates of the ratios $R (D^{(*)})$ , namely $R (D) = 0.296 (8)$ using final FNAL/MILC lattice results, and $R (D^{*}) = 0.261 (20)$ using preliminary JLQCD and FNAL/MILC lattice data. Our findings differ by $\sim 1.4 σ$ from the latest experimental determinations.

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Received 25 May 2021
Accepted 13 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.034503

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

G. Martinelli¹, S. Simula ², and L. Vittorio^3,4

¹Physics Department and INFN Sezione di Roma La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy
²Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
³Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
⁴Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy

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Issue

Vol. 105, Iss. 3 — 1 February 2022

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Physical Review D

covering particles, fields, gravitation, and cosmology