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

TL;DR

This paper investigates $CP$ violation in the decay $B^{\pm} ightarrow \pi^{\pm}\pi^{+}\pi^{-}$, focusing on forward-backward asymmetries and their interference effects, using LHCb data to reveal significant $CP$ asymmetries.

Contribution

It introduces a method to isolate $CP$ violation caused by interference of partial waves and provides experimental evidence of large $CP$ asymmetries in specific resonance regions.

Findings

Large $CP$ asymmetries observed in the $f_{0}(500)$-$ ho(770)^{0}$ region.

Interference of resonances significantly contributes to $CP$ violation.

Method effectively isolates direct $CP$ violation effects.

Abstract

$CP$ violation of the decay $B^{\pm}\rightarrow \pi^{\pm}\pi^{+}\pi^{-}$ 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 $B^{\pm}\rightarrow \pi^{\pm}\pi^{+}\pi^{-}$.