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

Abstract

Recent evidence for an approximately flavor-singlet assignment has strengthened the case for $X(2370)$ as a pseudoscalar glueball candidate. However, flavor singletness alone does not uniquely determine its constituent structure. Using calculated three-pseudoscalar decay ratios, we find that current data favor a flavor-singlet hybrid while remaining compatible with a trigluon glueball. More importantly, we identify two resonance-resolved ratios, $a_0(1450)\pi /[K_0^{\ast }(1430)\bar{K}+c.c.]$ and $\varphi \varphi /[b_1(1235)\rho ]$, whose predicted hierarchies place the compact-tetraquark, hybrid, and trigluon-glueball realizations in parametrically separated regions. These observables convert the constituent ambiguity of $X(2370)$ into a directly testable experimental question.