Probing Glueball content of X(2370) through heavy quarkonium radiative decays and electron-positron annihilation

Abstract: In this paper, we first analyze the light-cone distribution amplitudes of the pseudoscalar Glueball and point out that the two-gluon and quark-antiquark pair contributions naturally mix at the quantum loop level. Based on the $η-η&#39;-G-η<em>c$ tetra-mixing scheme and existing experimental results, we analyze the branching ratio of $J/ψ\to P+γ$ with pseudoscalar meson $P$ and extract the mixing parameters of the tetra-mixing scheme. We then successfully predict the branching ratio of $ψ(2S) \to P+γ$, which is found to be in good agreement with experimental results. We also find that the branching ratios of $J/ψ\to X(2370)+γ$ and $ψ(2S) \to X(2370)+γ$ are highly sensitive to the Glueball-charmonium mixing angle: the destructive mixing interference in the branching ratio of $J/ψ\to X(2370)+γ$ occurs at $φ</em>{gc}\approx0.01$, whereas that in $ψ(2S) \to X(2370)+γ$ occurs at $φ<em>{gc}\approx 0.11$. Moreover, the $J/ψ\to X(2370)+γ$ branching ratio exhibits constructive mixing interference when the mixing angle is larger than $φ</em>{gc}\approx 0.02$. Finally, we also study the electroproduction cross sections of pseudoscalar mesons. After excluding the resonance contributions, the theoretical calculations agree with the experimental measurements in order of magnitude, and we also present theoretical predictions for the electroproduction cross section of the $X(2370)$. These theoretical results can be readily tested by current BESIII and Belle-II experiments, and further experimental measurements will reveal the intrinsic nature of the $X(2370)$.