Eur. Phys. J. C (2024) 84: 358
https://doi.org/10.1140/epjc/s10052-024-12702-z

Regular Article - Theoretical Physics

The $B^0\to J/\psi f_0(1370,1500,1710)$ decays: an opportunity for scalar glueball hunting

¹ Department of Physics, Jiangsu Normal University, 221116, Xuzhou, China
² Department of Physics, Yantai University, 264005, Yantai, China
³ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, 210023, Nanjing, China

^c liuxin@jsnu.edu.cn

Received: 12 December 2023
Accepted: 20 March 2024
Published online: 4 April 2024

Abstract

The scalars $f_0$ closest to 1.5 GeV contain the mesons $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, and the latter two ones are usually viewed as the potential candidates for the scalar glueballs. In this work, by including the important contributions from the vertex corrections, we study the decays $B^0\to J/\psi f_0$ within the improved perturbative QCD approach and analyze the possible scalar glueball hunting. Together with the two mixing models, namely, $f_0(1500)(f_0(1710))$ being the primary scalar glueball in model I (II), and two classification scenarios, namely, $f_0$ being the $q\overline{q}$ excited (ground) states in scenario 1 (2), the branching fractions associated with their ratios for $B^0\to J/\psi f_0$ are evaluated comprehensively. The predictions with still large uncertainties in the considered two mixing models are roughly consistent with currently limited data, which indicates that both more rich data and more precise predictions are urgently demanded to figure out the scalar glueball clearly in the future. Moreover, several interesting ratios between the branching fractions of $B^0\to J/\psi f_0(\to {\pi }^{+}{\pi }^{-}/K^{+}{K}^{-})$ and $B^0\to J/\psi {\rho }^0/\varphi (\to {\pi }^{+}{\pi }^{-}/K^{+}{K}^{-})$ that could help us to understand the nature of scalar $f_0$ are defined and predicted theoretically. These ratios should be examined in future experiments.