Measurement of the branching fractions and longitudinal polarisations of $B^0_{(s)} \to K^{*0} \kern 0.18em \overline{\kern -0.18em K}{}^{*0}$ decays

TL;DR

This paper measures the branching fractions and longitudinal polarizations of specific B meson decays using LHCb data, confirming a significant tension with theoretical predictions in B to vector-vector decays.

Contribution

It provides the first detailed measurement of polarization fractions and decay ratios for $B^0$ and $B_s^0$ decays to $K^*$ mesons, highlighting discrepancies with theory.

Findings

Measured polarization fractions: $f_L^{d} = 0.600$ and $f_L^{s} = 0.159$.

Confirmed a 4.4 sigma tension between experiment and theory in $B o VV$ decays.

Provided precise ratios of decay amplitudes with detailed uncertainties.

Abstract

A time- and flavour-integrated amplitude analysis of $B^0$ and $B^0_s$ decays to the $(K^+\pi^-)(K^-\pi^+)$ final state in the $K^*(892)^0 \kern 0.18em \overline{\kern -0.18em K}{}^{*}(892)^0$ region is presented, using $pp$ collision data recorded with the LHCb detector in 2011--2018, corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$. The branching fractions of the $B^0$ and $B^0_s$ decays are measured relative to the $B^0 \to D^-\pi^+$ and $B^0_s \to D^-_s \pi^+$ modes, respectively. The corresponding longitudinal polarisation fractions are found to be $f_L^{d} = 0.600 \pm 0.022 \pm 0.017$ and $f_L^{s} = 0.159 \pm 0.010 \pm 0.007$, where the uncertainties are statistical and systematic, respectively. The theory-motivated ratio of the squared $B^0_s$ to $B^0$ longitudinally polarised decay amplitudes is found to be $L_{K^{*0} \kern 0.18em \overline{\kern -0.18em K}{}^{*0}} = 4.92 \pm 0.55 \pm 0.48 \pm 0.02 \pm 0.10$, where the uncertainties are statistical, systematic, due to uncertainty of external mass and lifetime measurements, and due to knowledge of the fragmentation fraction ratio, respectively. This confirms the previously reported tension between experimental determinations and theoretical predictions of longitudinal polarisation in $B \to VV$ decays at the level of 4.4 standard deviations.