The B⁰ → J/ψ f₀(1370,1500,1710) decays: an opportunity for scalar glueball hunting

The scalars f₀ f 0 closest to 1.5 GeV contain the mesons f₀(1370) f 0 ( 1370 ) , f₀(1500) f 0 ( 1500 ) and f₀(1710) 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 B⁰ → J/ψ f₀ B 0 → J / ψ f 0 within the improved perturbative QCD approach and analyze the possible scalar glueball hunting. Together with the two mixing models, namely, f₀(1500) (f₀(1710)) f 0 ( 1500 ) ( f 0 ( 1710 ) ) being the primary scalar glueball in model I (II), and two classification scenarios, namely, f₀ f 0 being the qq̄ q q ¯ excited (ground) states in scenario 1 (2), the branching fractions associated with their ratios for B⁰ → J/ψ f₀ B 0 → J / ψ 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 B⁰ → J/ψ f₀(→ π ⁺ π ⁻/K⁺ K⁻) B 0 → J / ψ f 0 ( → π + π - / K + K - ) and B⁰ → J/ψ ρ ⁰/φ (→ π ⁺ π ⁻/ K⁺ K⁻) B 0 → J / ψ ρ 0 / ϕ ( → π + π - / K + K - ) that could help us to understand the nature of scalar f₀ f 0 are defined and predicted theoretically. These ratios should be examined in future experiments.