Forward-backward asymmetry induced $CP$ asymmetry of $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$

Abstract

$CP$ violation of the decay $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the $f_0(500)-\rho (770{)}^0$ interfering region is analyzed. The forward-backward asymmetries (FBAs) and the corresponding $CP$ asymmetries FB-$CP$As are particularly investigated. To isolate the $CP$V caused by the interference of different partial wave more cleanly, we also introduce the direct-$CP$V-subtracted FB-$CP$A. Based on the LHCb data, we extract the FBAs, FB-$CP$As, direct-$CP$V-subtracted FB-$CP$A, as well as the regional $CP$As with invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair in the range 0.2 GeV/$c^2<\sqrt{s_{\text{low}}}<1.8$ GeV/$c^2$. It is found that the (direct-$CP$V-subtracted) FB-$CP$As are quite large in the $f_0(500)-\rho (770{)}^0$ interfering region, which confirms that the interference of the intermediate resonances $f_0(500)$ and $\rho (770{)}^0$ plays an important role for the $CP$ violation of the three-body decay channel $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$.

14 pages, 5 figures, 3 tables, version accepted by PRD

References in corpus (8)

• Observation of $CP$ violation in charm decays
• Measurements of $CP$ violation in the three-body phase space of charmless $B^{\pm }$ decays
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Measurement of CP observables in B+- --> D_CP K+- decays and constraints on the CKM angle gamma
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• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• A novel observable for $CP$ violation in multi-body decays and its application potential to charm and beauty meson decays
• Data-based analysis of Forward-Backward Asymmetry in $B^{\pm }\to K^{\pm }{K}^{\mp }{K}^{\pm }$

Cited by in corpus (2)

• Searching for $CP$ violation through two-dimensional angular distributions in four-body decays of bottom and charmed baryons
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays