A U-spin Puzzle in $B$ Decays

Abstract

We impose U spin symmetry ($SU(2{)}_{\mathrm{Uspin}}$) 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.

Comments: 5 pages, some clarifying remarks added, a number of references added. Accepted for publication