A U-spin Puzzle in $B$ Decays

TL;DR

This paper examines U-spin symmetry in B meson decays, revealing a significant discrepancy between expected and observed symmetry breaking, which may indicate new physics beyond the Standard Model.

Contribution

The study demonstrates that perfect U-spin symmetry does not fit the data and that large U-spin breaking is necessary, suggesting a potential new physics puzzle in B decays.

Findings

Perfect U-spin symmetry fit is very poor.

Large U-spin breaking (~100%) is required to explain data.

The results hint at possible new physics in B decays.

Abstract

We impose U spin symmetry ($SU(2)_{\rm Uspin}$) 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 $\Delta S=0$ processes $B^0 \to \pi^+\pi^-$, $B_s^0\to\pi^+ K^-$ and $B^0\to K^+ K^-$ form a U-spin triangle relation. The amplitudes for $B_s^0\to K^+ K^-$, $B^0\to\pi^- K^+$ and $B_s^0\to\pi^+\pi^-$ form a similar $\Delta S=1$ 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, the fit is very poor. If U-spin-breaking contributions are added, 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.