Open Access

Polarization fractions in $B \to V_{1} V_{2}$ : $U$ -spin constraints and new physics signatures

Debajyoti Choudhury^1,*, Suman Kumbhakar ^2,†, Anirban Kundu ^2,‡, and Soumitra Nandi ^3,§

¹Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
²Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India
³Department of Physics, Indian Institute of Technology, Guwahati 781039, India

^*Contact author: debajyoti.choudhury@gmail.com
^†Contact author: kumbhakar.suman@gmail.com
^‡Contact author: akphy@caluniv.ac.in
^§Contact author: soumitra.nandi@gmail.com

Phys. Rev. D 114, 015019 – Published 13 July, 2026

DOI: https://doi.org/10.1103/vxht-dclj

Abstract

We investigate the decays of $B$ mesons, i.e., $B_{d}$ , $B_{s}$ , $B^{+}$ , and their antiparticles, to two light vector mesons ( $B \to V_{1} V_{2}$ ). We use the SU(2) $U$ -spin symmetry, which relates $Δ S = 0$ and $Δ S = 1$ decay amplitudes through the interchange $d \leftrightarrow s$ and is an approximate symmetry of the Standard Model (SM), to relate the helicity amplitudes of these decays. Treating all the helicity amplitudes for these decays, and, hence, the reduced matrix elements, as free parameters, we find an acceptable solution within the SM, although this is driven by the fact that the number of observables is smaller than what is needed for a meaningful fit. To reduce the number of free parameters, we then use some apparently reasonable and theoretically motivated approximations, like the dominance of factorizable contributions over the nonfactorizable ones and, hence, a distinct hierarchy between the helicity amplitudes. We find that once the assumption of hierarchy is imposed, there is no solution, both in the exact $U$ -spin limit as well as when substantial $U$ -spin breaking is allowed for. The tension is primarily driven by the longitudinal polarization fractions in almost all $Δ S = 1$ decays, which are significantly smaller than the corresponding theoretical predictions based on the SM and $U$ -spin symmetry. This is particularly true for $B_{s} \to K^{* 0} \bar{K^{* 0}}$ , for which the individual disagreement with $U$ -spin-based expectation is more than $7 σ$ . Within the SM framework, the only effective resolution would be to entirely disregard the hierarchy between the longitudinal and transverse helicity amplitudes in the heavy-quark limit, as dictated by naive factorization, implying that there must be large nonfactorizable contributions to all these decay amplitudes. We also explore whether some new physics in the $b \to s$ sector that does not respect the hierarchy among the helicity amplitudes can reduce the tension for all the $Δ S = 1$ modes. While the answer is partially in the affirmative, we find that, for simplistic new physics scenarios, the tension still exists and the fit remains poor enough, if the hierarchy exists among the SM amplitudes. Some possible scenarios for a complete solution of the puzzle are also suggested.

Physics Subject Headings (PhySH)

Article Text

References (38)

N. B. Beaudry, A. Datta, D. London, A. Rashed, and J. S. Roux, The $B \to π K$ puzzle revisited, J. High Energy Phys. 01 (2018) 074.
A. Kundu, S. K. Patra, and S. Roy, Complete analysis of all $B \to π K$ decays, Phys. Rev. D 104, 095025 (2021).
Y. Amhis, Y. Grossman, and Y. Nir, The branching fraction of $B_{s}^{0} \to K^{0} {\bar{K}}^{0}$ : Three puzzles, J. High Energy Phys. 02 (2023) 113.
Y. Grossman, M. Neubert, Y. Nir, Y. Shpilman, and Y. Viernik, $B_{s} \to K^{0} {\bar{K}}^{0}$ beyond the standard model, J. High Energy Phys. 05 (2025) 210.
B. Bhattacharya, S. Kumbhakar, D. London, and N. Payot, U-spin puzzle in B decays, Phys. Rev. D 107, L011505 (2023).
R. Berthiaume, B. Bhattacharya, R. Boumris, A. Jean, S. Kumbhakar, and D. London, Anomalies in hadronic B decays, Phys. Rev. Lett. 133, 211802 (2024).
J. Davies, S. Schacht, N. Skidmore, and A. Soni, Reappraisal of SU(3)-flavor breaking in $B \to DP$ , Phys. Rev. D 109, 113006 (2024).
M. Burgos Marcos, M. Reboud, and K. K. Vos, Detailed $S U (3)$ flavour symmetry analysis of charmless two-body $B$ -meson decays including factorizable corrections, J. High Energy Phys. 03 (2026) 227.
Y. J. Shi, W. Wang, and J. Xu, On the equivalence of flavor SU(3) analyses of $B \to P P$ decays, Eur. Phys. J. C 85, 1283 (2025).
B. Bhattacharya, M. Bouchard, L. Hudy, A. Jean, D. London, and C. MacKenzie, Anomalies in hadronic $B$ decays: An update, Phys. Rev. D 112, 056014 (2025).
S. Schacht, A U-spin anomaly in charm $C P$ violation, J. High Energy Phys. 03 (2023) 205.
R. Bause, H. Gisbert, G. Hiller, T. Höhne, D. F. Litim, and T. Steudtner, U-spin-CP anomaly in charm, Phys. Rev. D 108, 035005 (2023).
C. Bolognani, U. Nierste, S. Schacht, and K. K. Vos, Anatomy of non-leptonic two-body decays of charmed mesons into final states with $η$ ’, J. High Energy Phys. 05 (2025) 148.
R. Sinha, T. E. Browder, N. G. Deshpande, D. Sahoo, and N. Sinha, Implications of the evidence for direct $CP$ violation in $D \to π^{+} π^{-}$ decays, Phys. Rev. D 113, 093003 (2026).
R. Aaij et al. (LHCb Collaboration), Amplitude analysis of the $B_{(s)}^{0} \to K^{* 0} {\bar{K}}^{* 0}$ decays and measurement of the branching fraction of the $B^{0} \to K^{* 0} {\bar{K}}^{* 0}$ decay, J. High Energy Phys. 07 (2019) 032.
Y. Yu, H. B. Fu, H. Zhang, and B. C. Ke, A phenomenological estimate of rescattering effects in $B_{s} \to K^{* 0} {\bar{K}}^{* 0}$ , Eur. Phys. J. C 85, 42 (2025).
R. Aaij et al. (LHCb Collaboration), Measurement of the branching fractions and longitudinal polarisations of $B_{(s)}^{0} \to K^{* 0} {\bar{K}}^{* 0}$ decays, Phys. Rev. D 113, 092002 (2026).
R. Aleksan and L. Oliver, ${\bar{B}}_{d, s} \to K^{* 0} {\bar{K}}^{* 0}$ decays, a serious problem for the standard model, arXiv:2312.07198.
R. Aleksan and L. Oliver, Analysis of data on $B$ decays into two light vector mesons, arXiv:2403.19025.
A. Biswas, S. Descotes-Genon, J. Matias, and G. Tetlalmatzi-Xolocotzi, A new puzzle in non-leptonic B decays, J. High Energy Phys. 06 (2023) 108.
A. Biswas, S. Descotes-Genon, J. Matias, and G. Tetlalmatzi-Xolocotzi, Optimised observables and new physics prospects in the penguin-mediated decays $B_{d (s)} \to K^{(*) 0} ϕ$ , J. High Energy Phys. 08 (2024) 030.
J. M. Lizana, J. Matias, and B. A. Stefanek, Explaining the $B_{d, s} \to K^{(*)} {\bar{K}}^{(*)}$ non-leptonic puzzle and charged-current B-anomalies via scalar leptoquarks, J. High Energy Phys. 09 (2023) 114.
A. Soni and D. A. Suprun, Determination of $γ$ from Charmless $B \to M_{1} M_{2}$ decays using U-spin, Phys. Rev. D 75, 054006 (2007).
M. Beneke, J. Rohrer, and D. Yang, Branching fractions, polarisation and asymmetries of $B \to V V$ decays, Nucl. Phys. B774, 64 (2007).
R. Aaij et al. (LHCb Collaboration), Measurement of $C P$ violation in $B_{s}^{0} \to ϕ ϕ$ decays, Phys. Rev. D 90, 052011 (2014).
R. Aaij et al. (LHCb Collaboration), Precision measurement of $C P$ violation in the Penguin-mediated decay $B_{s}^{0} \to ϕ ϕ$ , Phys. Rev. Lett. 131, 171802 (2023).
R. Aaij et al. (LHCb Collaboration), First observation of $C P$ violation and measurement of polarization in $B^{+} \to ρ (770)^{0} K^{*} (892)^{+}$ decays, Phys. Rev. Lett. 136, 021803 (2026).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
A. Dighe, A. Kundu, and S. Nandi, Possibility of large lifetime differences in neutral $B$ meson systems, Phys. Rev. D 76, 054005 (2007).
M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, QCD factorization in $B \to π K, π π$ decays and extraction of Wolfenstein parameters, Nucl. Phys. B606, 245 (2001).
G. Valencia, Angular correlations in the decay $B \to V V$ and $C P$ violation, Phys. Rev. D 39, 3339 (1989).
A. Datta and D. London, Triple-product correlations in $B \to V_{1} V_{2}$ decays and new physics, Int. J. Mod. Phys. A 19, 2505 (2004).
F. James and M. Roos, Minuit: A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10, 343 (1975).
F. James, MINUIT function minimization and error analysis: Reference manual version 94.1, Report No. CERN-D-506.
Heavy Flavor Averaging Group; Winter conferences (Moriond, etc.) 2024: https://hflav-eos.web.cern.ch/hflav-eos/triangle/moriond2024/.
C. Allton et al. (RBC-UKQCD Collaboration), Physical results from $2 + 1$ flavor domain wall QCD and SU(2) chiral perturbation theory, Phys. Rev. D 78, 114509 (2008).
F. Takahashi et al. (Particle Data Group), Review of particle physics, Int. J. Mod. Phys. A 41, 2630011 (2026).
A. Bharucha, D. M. Straub, and R. Zwicky, $B \to V ℓ^{+} ℓ^{-}$ in the standard model from light-cone sum rules, J. High Energy Phys. 08 (2016) 098.

Phys. Rev. D 114, 015019– Published 13 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 26 March 2026
Accepted 16 June 2026

DOI: https://doi.org/10.1103/vxht-dclj

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

Physical Review D

Reuse & Permissions

Export citation

Export citation

Polarization fractions in $B \to V_{1} V_{2}$ : $U$ -spin constraints and new physics signatures

Abstract

Physics Subject Headings (PhySH)

Article Text

References (38)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Polarization fractions in B→V1V2: U-spin constraints and new physics signatures

Abstract

Physics Subject Headings (PhySH)

Article Text

References (38)

Polarization fractions in $B \to V_{1} V_{2}$ : $U$ -spin constraints and new physics signatures