# $\phi\phi$ and $J/\psi\phi$ mass spectra in decay $B^0_s\to J/\psi\phi\phi$

## TL;DR

This paper models the mass spectra of $\,phi\,phi$ and $J/\,psi\,phi$ states in the decay $B_s^0 o J/\,psi\,phi\,phi$, incorporating various intermediate resonances and their mixings, to extract resonance properties.

## Contribution

It introduces a comprehensive model accounting for multiple resonances and their mixings in the decay, providing a method to extract resonance parameters from experimental spectra.

## Key findings

- Derived expressions for mass spectra including resonance mixings.
- Extracted resonance masses and coupling constants from spectra.
- Applied the model to recent LHCb data.

## Abstract

The mass spectra of the $\phi\phi$ and $J/\psi\phi$ states in the decay $B^0_s\to J/\psi\phi\phi$ recently observed by LHCb are calculated in the model which takes into account the $J^P=0^+,0^-,2^+$ intermediate resonances $R_1$, $R_2$ in the $\phi\phi$ channel and the $J^P=1^+$ ones, $X_1$, $X_2$, in the $J/\psi\phi$ channel. When obtaining the expressions for the effective amplitudes and mass spectra, the approximate threshold kinematics of the decay is used essentially. The $R_1-R_2$ and $X_1-X_2$ mixings arising due to the common decay modes $\phi\phi$ and $J/\psi\phi$, respectively, are also taken into account. The obtained expressions for the mass spectra are applied for extracting the information about masses and coupling constants of the resonances in the $\phi\phi$ and $J/\psi\phi$ final states.