# Phenomenological studies on the $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays

## TL;DR

This paper extends perturbative QCD calculations to specific B meson decays involving scalar mesons, comparing predictions with experimental data and exploring observables to constrain mixing angles and flavor symmetry breaking.

## Contribution

It provides the first next-to-leading order perturbative QCD analysis of $B_{d,s}^0$ decays to $J/$ and scalar mesons $f_0(500)$ and $f_0(980)$, including predictions for branching ratios.

## Key findings

- Branching ratios generally agree with data within uncertainties.
- Predicted ${
m BR}(B_{d}^0 o J/ f_0(980) o K^+ K^-)$ is approximately 5.8e-7.
- Predicted ${
m BR}(B_{s}^0 o J/ f_0(980) o K^+ K^-)$ is approximately 4.6e-5.

## Abstract

Encouraged by the global agreement between theoretical predictions and experimental measurements for $B \to J/\psi V$ decays, we extend that perturbative QCD formalism to $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of $f_0(500)$ and $f_0(980)$. With the angle $\phi_f \approx 25^\circ$ of the $f_0(500)-f_0(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the $B_d^0 \to J/\psi f_0(500) (\to \pi^+ \pi^-)$ and $B_{d,s}^0 \to J/\psi f_0(980) (\to \pi^+ \pi^-)$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging $B_s^0 \to J/\psi f_0(500) (\to \pi^+\pi^-)$ one. Then, we further explore the relevant observables of the $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays, which could provide further constraints on the mixing angle $\phi_f$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict ${\rm BR}(B_{d}^0 \to J/\psi f_0(980)(\to K^+ K^-))=5.8^{+3.1}_{-2.9} \times 10^{-7}$ and ${\rm BR}(B_{s}^0 \to J/\psi f_0(980)(\to K^+ K^-)) =4.6^{+2.6}_{-2.3} \times 10^{-5}$. All theoretical predictions await the future examinations with high precision.