Newly observed $a_0(1817)$ as the scaling point of constructing the scalar meson spectroscopy
Stimulated by the newly observed $a_0(1817)$ by the BESIII Collaboration, we find a perfect Regge trajectory composed of the $a_0(980)$, $a_0(1450)$, and $a_0(1817)$, which leads us to categorize the $a_0(980)$, $a_0(1450)$, and $a_0(1817)$ into the isovector scalar meson family. This scenario is supported by their two-body Okubo-Zweig-Iizuka allowed strong decay behaviors. In this scheme, we also predict the third radial excitation of the $a_0(980)$, which is denoted as the $a_0(2115)$, accessible at future experiment as a direct test of this assignment. We find another Regge trajectory which contains three isoscalar scalar states $f_0(980)$, $X(1812)$, and $f_0(2100)$. We investigate their two-body Okubo-Zweig-Iizuka allowed strong decay patterns, which are roughly consistent with the experimental data. The $f_0(980)$, $X(1812)$, and $f_0(2100)$ can be well grouped into the isoscalar scalar meson family. We want to emphasize that these two Regge trajectories have a similar slope. In summary, the present work provides a scheme of constructing the scalar meson family based on these reported scalar states. The possibility of the $f_0(1710)$ as the candidate of the scalar glueball cannot be excluded by the observation of the $a_0(1817)$ since the $a_0(1817)$ is more suitable as the isovector partner of the $X(1812)$.