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

We carry out a $U$-spin symmetry analysis for CP violation in $B^-$ decays into three light $π^-π^-π^+$, $π^- K^-K^+$, $K^-K^-K^+$ and $K^- π^-π^+$ 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.

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