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

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## 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.

## Figures and captions

 Dalitz-plot distributions for (a) $B ^+$ and (b) $B ^-$ candidate decays to $\pi ^\pm \pi ^+ \pi ^-$. Depleted regions are due to the $\overline{ D }{} {}^0$ veto. Fig1a.pdf [331 KiB] HiDef png [269 KiB] Thumbnail [115 KiB] *.C file Fig1b.pdf [362 KiB] HiDef png [293 KiB] Thumbnail [123 KiB] *.C file Projections of data and fits (top) on $m_{\rm low}$ in (a) the low $m(\pi ^+ \pi ^- )$ region and (b) the $\rho$--$\omega$ region, with (bottom) the corresponding $C P$ asymmetries in these ranges. Fig2a.pdf [38 KiB] HiDef png [308 KiB] Thumbnail [244 KiB] *.C file Fig2b.pdf [44 KiB] HiDef png [405 KiB] Thumbnail [296 KiB] *.C file Projections of the $C P$ asymmetry for data and fits as a function of $\cos\theta_{\rm hel}$ in the regions (a) below and (b) above the $\rho(770)^0$ resonance pole. Fig3.pdf [34 KiB] HiDef png [406 KiB] Thumbnail [288 KiB] *.C file Projections of data and fits (top) on $m_{\rm low}$ in the $f_2(1270)$ mass region, with (bottom) the corresponding $C P$ asymmetry. Fig4.pdf [40 KiB] HiDef png [362 KiB] Thumbnail [282 KiB] *.C file Animated gif made out of all figures. PAPER-2019-018.gif Thumbnail

## Tables and captions

 Results for $C P$ -conserving fit fractions, quasi-two-body $C P$ asymmetries, and phases for each component relative to the combined $\rho(770)^0$--$\omega(782)$ model, given for each S-wave approach. The $\rho(770)^0$ and $\omega(782)$ values are extracted from the combined $\rho(770)^0$--$\omega(782)$ mixing model. The first uncertainty is statistical while the second is systematic. Table_1.pdf [69 KiB] HiDef png [139 KiB] Thumbnail [65 KiB] tex code

Created on 20 February 2021.