U-spin analysis of CP violation in $B^{-}$ decays into three charged light pseudoscalar mesons

Abstract

We carry out a $U$-spin symmetry analysis for CP violation in $B^{-}$ decays into three light ${\pi }^{-}{\pi }^{-}{\pi }^{+}$, ${\pi }^{-}{K}^{-}{K}^{+}$, $K^{-}{K}^{-}{K}^{+}$ and $K^{-}{\pi }^{-}{\pi }^{+}$ mesons. We clarify some subtle points in constructing decay amplitudes with $U=0$ formed by the two negatively charged light mesons in the final states. $U$-spin conserving momentum independent and momentum dependent decay amplitudes, and $U$-spin violating decay amplitudes due to quark mass difference are constructed.

Comments: RevTex 12 pages wit no figure