CP Violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ and $B^{\pm }\to \sigma {\pi }^{\pm }$ Decays

Abstract

The decay amplitude of $B^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ in the Dalitz plot has been analyzed by the LHCb using three different approaches for the $S$-wave component. It was found that the mode with $\sigma$ (or $f_0(500)$) exhibited a CP asymmetry of 15\% in the isobar model, whereas the $f_2(1270)$ mode had a 40\% asymmetry. On the contrary, CP asymmetry for the dominant quasi-two-body decay $B^{-}\to {\rho }^0{\pi }^{-}$ was found to be consistent with zero in all three approaches, while all the existing theoretical predictions lead to a negative CP asymmetry ranging from $-7\%$ to $-45\%$. We show that the nearly vanishing CP violation in $B^{-}\to {\rho }^0{\pi }^{-}$ is understandable in the framework of QCD factorization (QCDF). It arises from the $1/m_b$ power corrections to the penguin amplitudes due to penguin annihilations and to the color-suppressed tree amplitude due to hard spectator interactions. Penguin annihilation and hard spectator interactions contribute destructively to $A_{CP}(B^{-}\to {\rho }^0{\pi }^{-})$ to render it consistent with zero. The branching fraction and CP asymmetry in $B^{-}\to \sigma /f_0(500){\pi }^{-}$ are investigated in QCDF with results in agreement with experiment.

Comments: 11 pages