Construction of Isoscalar $2^{-+}$ Mesonic States Inspired by the $X(2600)$ Discovery

The BESIII observation of the $X(2600)$ suggests that one possible assignment for its spin-parity quantum numbers is $J^{PC}=2^{-+}$. This finding motivates us to systematically revisit isoscalar pseudotensor mesonic states through a comprehensive spectroscopic study. In this work, we employ a potential model to calculate the mass spectrum of isoscalar pseudotensor meson states with varying radial quantum numbers. Additionally, we analyze their strong decay behaviors, as allowed by the Okubo-Zweig-Iizuka (OZI) rule, using the quark pair creation model. Our findings yield valuable information about their resonant parameters and partial decay widths, which can aid in identifying the observed isoscalar pseudotensor states when combined with current experimental data. Importantly, we also predict several radial excitations of isoscalar pseudotensor mesons that remain unobserved experimentally. Furthermore, we exclude the $X(2600)$ from being classified as an isoscalar pseudotensor meson, which is critical for elucidating the properties of the $X(2600)$.