The Nonresonant Cabibbo Suppressed Decay $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ and Signal for CP Violation

Abstract

We consider various contributions to the nonresonant decay $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$, both of the long-distance and short-distance types with the former providing for most of the branching ratio, predicted to be $BR(B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm })=(1.5-8.4)\times 10^{-5}$. We also discuss an application to CP violation resulting from the interference of that nonresonant background (with $m({\pi }^{+}{\pi }^{-})\approx 3.4$ GeV) and $B^{\pm }\to {\chi }_{c0}{\pi }^{\pm }$ followed by ${\chi }_{c0}\to {\pi }^{+}{\pi }^{-}$. The resulting value of the partial rate asymmetry is $(0.40\sim 0.48)\mbox{sin}γ$, where $γ= \mbox{arg}(V_{ub}^*)$.

10 pages, Revtex

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