Final state interaction on $B^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$

Abstract

The large localized CP asymmetries observed by LHCb in three-body charmless decays of $B$ mesons brings new challenge for experimentalists and their traditional models to fit data. With higher statistics, rescattering and three-body effects, previously ignored on data analysis, become more visible. The time is ripe to use better theoretical assumptions as an ingredient in order to improve the analysis. In this paper we address the issue of rescattering effects in the charmless three-body decays of $B$ mesons. In particular, we study the case of the $B^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay and show that the presence of hadronic loops shifts the P-wave phase near threshold to below zero, and modify the position of the $\rho$-meson peak and it width, in the Dalitz plot.

Cited by in corpus (14)

• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• Direct CP violation in beauty and charm hadron decays
• Will the subprocesses $\rho (770,1450{)}^0\to K^{+}{K}^{-}$ contribute large branching fractions for $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays?
• Virtual contributions from $D^{\ast }(2007{)}^0$ and $D^{\ast }(2010{)}^{\pm }$ in the $B\to D\pi h$ decays
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• $S$, $P$ and $D$-wave resonance contributions to $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays in the perturbative QCD approach
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach