Studying $X(2100)$ hadronic decays and predicting its pion and kaon induced productions

The newly observed $X(2100)$ by the BESIII Collaboration inspires our interest in studying the light meson system, especially axial-vector mesons. Since the $X(2100)$ has $J^P=1^+$ possibilities but cannot be distinguished only by mass, we make use of flux-tube model to study the strong decay behavior of $X(2100)$ under this assignment. The experimental width of the newly reported $X(2100)$ can be reproduced in our calculation, which favors an assignment of $X(2100)$ as the second radial excitation of $h_1(1380)$ with $I(J^P)=0(1^+)$. And the $\mathcal{B}(X(2100)\to \phi \eta^\prime)$ has a sizable contribution to the total width. Furthermore, we focus on the production of $X(2100)$ and its flavour partner $h_1(1965)$ induced by pion and kaon on a proton target with the Feynman model and the Regge model, which is an available platform to further identify their nature. The numerical results indicate that the total cross section are similar in the two models. When the range of momentum ${\mathrm{p_{Lab}}}$ is 10 to 30 GeV/$c$, the total cross sections for $\pi^-p\to X(2100)n$ and $K^-p\to X(2100)\Lambda$ are predicted to be at an order of magnitude of 0.1 $\mu$b. Whereas, the total cross section for $\pi^-p\to h_1(1965)n$ is near an order of magnitude of 10 $\mu$b when $p_{\mathrm{Lab}}$ is from 10 to 30 GeV/$c$, and much larger than that of reaction $K^-p\to h_1(1965)\Lambda$. These predictions can provide some valuable information to search for $X(2100)$ and $h_1(1965)$ in experiments at J-PARC, COMPASS, OKA@U-70 and SPS@CERN.