Decipher the nature of glueball candidate $X(2370)$

RESUMO

As a unique form of matter composed entirely of gauge bosons, glueballs are an important low-energy prediction of QCD. After decades of searches, the BESIII Collaboration recently suggested that $X(2370)$ may contain a dominant glueball component, based largely on evidence that it is approximately a flavor singlet. Recognizing that flavor-singlet character does not uniquely identify a glueball, we perform a comprehensive analysis using available mass, flavor-singlet, and decay constraints. We find that three flavor-singlet configurations-hybrid meson, tetraquark state, and trigluon glueball-can satisfactorily reproduce the existing experimental data. Among these possibilities, the hybrid structure best describes the measured three-pseudoscalar decay ratios. To ultimately pin down the dominant structure of $X(2370)$, we propose measuring the decay-width ratios $a_0(1450)\pi/[K_0^*(1430)\bar K+\mathrm{c.c.}]$ and $\phi\phi/[b_1(1235)\rho]$, which can exclusively distinguish these three scenarios.