Study of the $B^0\to ρ(770)^0 K^*(892)^0$ decay with an amplitude analysis of $B^0\to (π^+π^-) (K^+π^-)$ decays

Abstract

An amplitude analysis of ${B^0\to (π^+π^-) (K^+π^-)}$ decays is performed in the two-body invariant mass regions ${300 < m(π^+π^-)<1100}$ MeV/$c^2$, accounting for the $ρ^0$, $ω$, $f_0(500)$, $f_0(980)$ and $f_0(1370)$ resonances, and ${750 < m(K^+π^-)<1200}$ MeV/$c^2$, which is dominated by the $K^{*}(892)^0$ meson. The analysis uses 3 fb$^{-1}$ of proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The $CP$ averages and asymmetries are measured for the magnitudes and phase differences of the contributing amplitudes. The $CP$-averaged longitudinal polarisation fractions of the vector-vector modes are found to be $\tilde{f}^0_{ρK^{*}} = 0.164 \pm 0.015 \pm 0.022$ and $\tilde{f}^0_{ωK^{*}} = 0.68 \pm 0.17 \pm 0.16$, and their $CP$ asymmetries, $\mathcal{A}^0_{ρK^{*}} = -0.62 \pm 0.09 \pm 0.09$ and $\mathcal{A}^0_{ωK^{*}} = -0.13 \pm 0.27 \pm 0.13$, where the first uncertainty is statistical and the second systematic.

All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2018-042.html (LHCb public pages)