Observation of several sources of $CP$ violation in $B^+ \to \pi^+ \pi^+ \pi^-$ decays

TL;DR

This paper reports the observation of multiple sources of $CP$ violation in $B^+ o \pi^+\pi^+\pi^-$ decays, revealing complex interference effects and asymmetries in decay amplitudes based on LHCb data.

Contribution

It presents the first detailed amplitude analysis identifying several sources of $CP$ violation in three-body $B^+$ decays, including tensor resonance and S-wave contributions.

Findings

Large $CP$ asymmetry in $f_2(1270)$ resonance amplitude

Significant $CP$ violation in low-mass $\pi^+\pi^-$ S-wave

Interference effects cause local asymmetries that cancel globally

Abstract

Observations are reported of different sources of $CP$ violation from an amplitude analysis of $B^+ \to \pi^+ \pi^+ \pi^-$ decays, based on a data sample corresponding to an integrated luminosity of $3 \; {\rm fb}^{-1}$ of $pp$ collisions recorded with the LHCb detector. A large $CP$ asymmetry is observed in the decay amplitude involving the tensor $f_2(1270)$ resonance, and in addition significant $CP$ violation is found in the $\pi^+ \pi^-$ S-wave at low invariant mass. The presence of $CP$ violation related to interference between the $\pi^+ \pi^-$ S-wave and the P-wave $B^+ \to \rho(770)^0 \pi^+$ amplitude is also established; this causes large local asymmetries but cancels when integrated over the phase space of the decay. The results provide both qualitative and quantitative new insights into $CP$-violation effects in hadronic $B$ decays.