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Exclusive semileptonic $B$ decays to the ground and excited states of light mesons

V. O. Galkin ^*

Xian-Wei Kang^†

Federal Research Center “Computer Science and Control” Russian Academy of Sciences, Vavilov Street 40, Moscow, 119333, Russian Federation

Key Laboratory of Beam Technology of the Ministry of Education, School of Physics and Astronomy, Beijing Normal University, Beijing 100875, People’s Republic of China

^*Contact author: vgalkin@frccsc.ru
^†Contact author: xwkang@bnu.edu.cn

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Phys. Rev. D 113, 073001 – Published 1 April, 2026

DOI: https://doi.org/10.1103/43c9-kssx

Abstract

Exclusive semileptonic decays of $B$ mesons to the ground, radially and orbitally excited states of light mesons are investigated in the framework of the relativistic quark model based on the quasipotential approach. Such decays are very important for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $| V_{u b} |$ and testing the nature of the excited light mesons. The mixing schemes for the isoscalar light mesons are considered. The possible assignment of the experimentally observed excited light mesons to the particular states is discussed. The form factors parametrizing weak decay matrix elements between the initial $B$ meson and final light mesons are calculated with the complete account of the relativistic effects, including contributions of the intermediate negative energy states and relativistic transformations of the meson wave functions from rest to the moving reference frame. As a result, the transferred momentum squared, $q^{2}$ , dependence of the form factors is explicitly determined in the whole accessible kinematical range. On the basis of the helicity formalism, the decay branching fractions and asymmetry and polarization parameters are calculated. The obtained results for the semileptonic $B$ decays to the ground states of light mesons are confronted with available experimental data. On this basis, the value of the $| V_{u b} |$ matrix element is determined. It is found in good agreement with the value extracted from inclusive decays. Predictions for the branching fractions of the semileptonic $B$ decays to radially ( $2 S$ and $3 S$ ) and orbitally ( $1 P$ and $2 P$ ) excited light mesons are given. Comparison with the previous calculations is performed. It is found that several decays to the excited light mesons ( $B \to ρ (1450) l ν_{l}$ , $B \to b_{1} (1235) l ν_{l}$ , $B \to a_{1} (1260) l ν_{l}$ , $B \to h_{1} (1170) l ν_{l}$ , $B \to a_{2} (1320) l ν_{l}$ , $B \to a_{2} (1700) l ν_{l}$ ) have branching fractions of the order $10^{- 4}$ and, thus, they can be measured at existing and future $B$ factories.

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References (45)

N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10, 531 (1963).
M. Kobayashi and T. Maskawa, $C P$ violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
M. Fael, M. Prim, and K. K. Vos, Inclusive $B \to X_{c} ℓ {\bar{ν}}_{ℓ}$ and $B \to X_{u} ℓ {\bar{ν}}_{ℓ}$ decays: Current status and future prospects, Eur. Phys. J. Special Topics 233, 325 (2024).
S. Banerjee et al. (Heavy Flavor Averaging Group (HFLAV), Averages of $b$ -hadron, $c$ -hadron, and $τ$ -lepton properties as of 2023, Phys. Rev. D 113, 012008 (2026).
X.-W. Kang, B. Kubis, C. Hanhart, and U.-G. Meißner, $B_{l 4}$ decays and the extraction of $| V_{u b} |$ , Phys. Rev. D 89, 053015 (2014).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
J. R. Pelaez, Light meson resonances, arXiv:2509.08648.
D. Ebert, R. N. Faustov, and V. O. Galkin, Properties of heavy quarkonia and $B_{c}$ mesons in the relativistic quark model, Phys. Rev. D 67, 014027 (2003).
R. N. Faustov, V. O. Galkin, and X.-W. Kang, Semileptonic decays of $D$ and $D_{s}$ mesons in the relativistic quark model, Phys. Rev. D 101, 013004 (2020).
V. O. Galkin and I. S. Sukhanov, Exclusive semileptonic decays of $D$ and $D_{s}$ mesons into orbitally and radially excited states of strange and light mesons, Phys. Rev. D 111, 093001 (2025).
D. Ebert, R. N. Faustov, and V. O. Galkin, Analysis of semileptonic $B$ decays in the relativistic quark model, Phys. Rev. D 75, 074008 (2007).
D. Ebert, R. N. Faustov, and V. O. Galkin, Exclusive semileptonic and nonleptonic decays of $B$ mesons to orbitally excited light mesons, Phys. Rev. D 85, 054006 (2012).
R. N. Faustov, V. O. Galkin, and X.-W. Kang, Relativistic description of the semileptonic decays of bottom mesons, Phys. Rev. D 106, 013004 (2022).
D. Ebert, R. N. Faustov, and V. O. Galkin, Heavy-light meson spectroscopy and Regge trajectories in the relativistic quark model, Eur. Phys. J. C 66, 197 (2010).
D. Ebert, R. N. Faustov, and V. O. Galkin, Mass spectra and Regge trajectories of light mesons in the relativistic quark model, Phys. Rev. D 79, 114029 (2009).
R. Fleischer, R. Knegjens, and G. Ricciardi, Exploring $C P$ violation and $η − η^{'}$ mixing with the $B_{s, d}^{0} \to J / ψ η^{(')}$ systems, Eur. Phys. J. C 71, 1798 (2011).
C. Di Donato, G. Ricciardi, and I. Bigi, $η − η^{'}$ mixing—from electromagnetic transitions to weak decays of charm and beauty hadrons, Phys. Rev. D 85, 013016 (2012).
R. Aaij et al. (LHCb Collaboration), Improved measurement of $η / η^{'}$ mixing in $B_{(s)}^{0} \to J / ψ η^{(')}$ decays, J. High Energy Phys. 10 (2025) 113.
M. Gronau and J. L. Rosner, $ω - ϕ$ mixing and weak annihilation in $D_{(s)}$ decays, Phys. Rev. D 79, 074006 (2009).
A. Kucukarslan and U.-G. Meissner, $ω - ϕ$ mixing in chiral perturbation theory, Mod. Phys. Lett. A 21, 1423 (2006).
F. Ambrosino et al., A Global fit to determine the pseudoscalar mixing angle and the gluonium content of the eta-prime meson, J. High Energy Phys. 07 (2009) 105.
D. Ebert, R. N. Faustov, and V. O. Galkin, Masses of light tetraquarks and scalar mesons in the relativistic quark model, Eur. Phys. J. C 60, 273 (2009).
H.-Y. Cheng, C.-K. Chua, and K.-F. Liu, Scalar glueball, scalar quarkonia, and their mixing, Phys. Rev. D 74, 094005 (2006).
H.-Y. Cheng, C.-K. Chua, and K.-F. Liu, Revisiting scalar glueballs, Phys. Rev. D 92, 094006 (2015).
A. A. Petrov, Glueball-meson molecules, Phys. Lett. B 843, 138030 (2023).
E. Klempt, Scalar mesons and the fragmented glueball, Phys. Lett. B 820, 136512 (2021).
E. Klempt and A. V. Sarantsev, Singlet-octet-glueball mixing of scalar mesons, Phys. Lett. B 826, 136906 (2022).
E. Klempt, Glueballs, a fulfilled promise of QCD?, arXiv:2211.12901.
H.-Y. Cheng, Revisiting axial-vector meson mixing, Phys. Lett. B 707, 116 (2012).
H.-Y. Cheng, Mixing angle of $K_{1}$ axial vector mesons, Proc. Sci. Hadron2013 (2013) 090 [arXiv:1311.2370].
H.-Y. Cheng and R. Shrock, Some results on vector and tensor meson mixing in a generalized QCD-like theory, Phys. Rev. D 84, 094008 (2011).
D.-M. Li, H. Yu, and Q.-X. Shen, Properties of the tensor mesons $f_{2} (1270)$ and $f_{2}^{'} (1525)$ , J. Phys. G 27, 807 (2001).
Y. Li, A.-J. Ma, Z. Rui, W.-F. Wang, and Z.-J. Xiao, Quasi-two-body decays $B_{(s)} \to P f_{2} (1270) \to P π π$ in the perturbative QCD approach, Phys. Rev. D 98, 056019 (2018).
D. Ebert, R. N. Faustov, and V. O. Galkin, Weak decays of the $B_{c}$ meson to charmonium and $D$ mesons in the relativistic quark model, Phys. Rev. D 68, 094020 (2003).
D. Ebert, R. N. Faustov, and V. O. Galkin, Semileptonic and nonleptonic decays of $B_{c}$ mesons to orbitally excited heavy mesons in the relativistic quark model, Phys. Rev. D 82, 034019 (2010).
M. A. Ivanov, J. G. Körner, J. N. Pandya, P. Santorelli, N. R. Soni, and C.-T. Tran, Exclusive semileptonic decays of $D$ and $D_{s}$ mesons in the covariant confining quark model, Front. Phys. (Beijing) 14, 64401 (2019).
I. Adachi et al. (Belle-II Collaboration), Determination of $| V_{u b} |$ from simultaneous measurements of untagged $B^{0} \to π^{-} ℓ^{+} ν_{ℓ}$ and $B^{+} \to ρ^{0} ℓ^{+} ν_{ℓ}$ decays, Phys. Rev. D 111, 112009 (2025).
X.-W. Kang, T. Luo, Y. Zhang, L.-Y. Dai, and C. Wang, Semileptonic $B$ and $B_{s}$ decays involving scalar and axial-vector mesons, Eur. Phys. J. C 78, 909 (2018).
Y. Qiao, J.-H. Sheng, Y.-G. Xu, and R.-M. Wang, Flavor SU(3) analysis of the charmless semileptonic $B \to P V ℓ^{+} ν_{ℓ}$ decays, Phys. Rev. D 112, 033002 (2025).
R.-H. Li, C.-D. Lu, W. Wang, and X.-X. Wang, $B \to S$ transition form factors in the PQCD approach, Phys. Rev. D 79, 014013 (2009).
R.-H. Li, C.-D. Lu, and W. Wang, Transition form factors of $B$ decays into $p$ -wave axial-vector mesons in the perturbative QCD approach, Phys. Rev. D 79, 034014 (2009).
W. Wang, $B$ to tensor meson form factors in the perturbative QCD approach, Phys. Rev. D 83, 014008 (2011).
Y.-M. Wang, M. J. Aslam, and C.-D. Lu, Scalar mesons in weak semileptonic decays of $B_{(s)}$ , Phys. Rev. D 78, 014006 (2008).
K.-C. Yang, Form-factors of $B_{(u, d, s)}$ decays into $P$ -wave axial-vector mesons in the light-cone sum rule approach, Phys. Rev. D 78, 034018 (2008).
Z.-G. Wang, Analysis of the $B \to K_{2}^{*} (1430), a_{2} (1320), f_{2} (1270)$ form-factors with light-cone QCD sum rules, Mod. Phys. Lett. A 26, 2761 (2011).

Phys. Rev. D 113, 073001– Published 1 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 17 November 2025
Accepted 24 February 2026

DOI: https://doi.org/10.1103/43c9-kssx

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.

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Exclusive semileptonic $B$ decays to the ground and excited states of light mesons

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Exclusive semileptonic B decays to the ground and excited states of light mesons

Abstract

Physics Subject Headings (PhySH)

Article Text

References (45)

Exclusive semileptonic $B$ decays to the ground and excited states of light mesons