The Nonresonant Cabibbo Suppressed Decay B±→ π+π-π± and Signal for CP Violation

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We consider various contributions to the nonresonant decay B±→ π+π-π±, both of the long-distance and short-distance types with the former providing for most of the branching ratio, predicted to be BR(B±→ π+π-π±) = (1.5 - 8.4)× 10⁻⁵. We also discuss an application to CP violation resulting from the interference of that nonresonant background (with m(π+π-)≈ 3.4 GeV) and B±→ χc₀ π± followed by χc₀→ π+π-. The resulting value of the partial rate asymmetry is (0.40 0.48)sinγ, where γ= arg(Vub*).