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

## TL;DR

This paper performs an amplitude analysis of B0 decays into specific meson pairs, measuring CP asymmetries and polarization fractions using LHCb data, providing insights into decay dynamics and CP violation.

## Contribution

It introduces a detailed amplitude analysis of B0 to meson pairs with resonance contributions, including CP asymmetries and polarization measurements, using 3 fb^{-1} of LHCb data.

## Key findings

- Measured CP-averaged longitudinal polarization fractions: 0.164 and 0.68.
- Observed CP asymmetries: -0.62 and -0.13.
- Analyzed resonance contributions in B0 decays.

## Abstract

An amplitude analysis of ${B^0\to (\pi^+\pi^-) (K^+\pi^-)}$ decays is performed in the two-body invariant mass regions ${300 < m(\pi^+\pi^-)<1100}$ MeV/$c^2$, accounting for the $\rho^0$, $\omega$, $f_0(500)$, $f_0(980)$ and $f_0(1370)$ resonances, and ${750 < m(K^+\pi^-)<1200}$ 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 $\tilde{f}^0_{\rho K^{*}} = 0.164 \pm 0.015 \pm 0.022$ and $\tilde{f}^0_{\omega K^{*}} = 0.68 \pm 0.17 \pm 0.16$, and their $CP$ asymmetries, $\mathcal{A}^0_{\rho K^{*}} = -0.62 \pm 0.09 \pm 0.09$ and $\mathcal{A}^0_{\omega K^{*}} = -0.13 \pm 0.27 \pm 0.13$, where the first uncertainty is statistical and the second systematic.