First observation of $CP$ violation and measurement of polarization in $B^+\to\rho(770)^0 K^*(892)^+$ decays

Abstract

An amplitude analysis of the $B^+\to(\pi^+\pi^-)(K^0_{\mathrm{S}}\pi^+)$ decay is performed in the mass regions $0.30 < m_{\pi^+\pi^-} < 1.10\,\mathrm{GeV}/c^2$ and $0.75 < m_{K^0_{\mathrm{S}}\pi^+} < 1.20\,\mathrm{GeV}/c^2$, using $pp$ collision data recorded with the LHCb detector corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$. The polarization fractions and $CP$ asymmetries for $B^+\to\rho(770)^0K^*(892)^+$ decays are measured. Violation of the $CP$ symmetry in the decay $B^+\to\rho(770)^0K^*(892)^+$ is observed for the first time, with a significance exceeding nine standard deviations. The $CP$ asymmetry is measured to be ${\cal A}_{CP} = 0.507 \pm 0.062\ \text{(stat)} \pm 0.024\ \text{(syst)}$ and the $CP$-averaged longitudinal polarization fraction of $f_L = 0.720 \pm 0.028\ \text{(stat)} \pm 0.009\ \text{(syst)}$. The measurements help to shed light on the polarization puzzle of $B$ mesons decaying to two vector mesons.