Letter
Open Access

$U$ -spin puzzle in $B$ decays

Bhubanjyoti Bhattacharya ^1,*, Suman Kumbhakar^2,†, David London ^2,‡, and Nicolas Payot ^2,§

¹Department of Natural Sciences, Lawrence Technological University, Southfield, Michigan 48075, USA
²Physique des Particules, Université de Montréal, Montréal, Quebec H2V 0B3, Canada

^*bbhattach@ltu.edu
^†suman.kumbhakar@umontreal.ca
^‡london@lps.umontreal.ca
^§nicolas.payot@umontreal.ca

Phys. Rev. D 107, L011505 – Published 27 January, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L011505

Abstract

We impose $U$ -spin symmetry [ $S U (2)_{Uspin}$ ] on the Hamiltonian for $B$ decays. As expected, we find the equality of amplitudes related by the exchange $d \leftrightarrow s$ . We also find that the amplitudes for the $Δ S = 0$ processes $B^{0} \to π^{+} π^{-}$ , $B_{s}^{0} \to π^{+} K^{-}$ , and $B^{0} \to K^{+} K^{-}$ form a $U$ -spin triangle relation. The amplitudes for $B_{s}^{0} \to K^{+} K^{-}$ , $B^{0} \to π^{-} K^{+}$ , and $B_{s}^{0} \to π^{+} π^{-}$ form a similar $Δ S = 1$ triangle relation. And these two triangles are related to one another by $d \leftrightarrow s$ . We perform fits to the observables for these six decays. If perfect $U$ spin is assumed, then the fit is very poor. If $U$ -spin-breaking contributions are added, then we find many scenarios that can explain the data. However, in all cases, 100% $U$ -spin breaking is required, considerably larger than the naive expectation of $\sim 20 %$ . This is the $U$ -spin puzzle; it may be strongly hinting at the presence of new physics.

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Phys. Rev. D 107, L011505– Published 27 January, 2023

Vol. 107, Iss. 1 — 1 January 2023

Received 21 November 2022
Accepted 5 January 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L011505

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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$U$ -spin puzzle in $B$ decays

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U-spin puzzle in B decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (22)

$U$ -spin puzzle in $B$ decays