Exploring kaon induced reactions for unraveling the nature of the scalar meson $a_0(1817)$

In this study, we comprehensively investigate the production of isovector scalar meson $a_0(1817)$ using the effective Lagrangian approach. Specifically, we employ the Reggeized $t$ channel Born term to calculate the total and differential cross sections for the reaction $K^{-}p\to a_0(1817)\mathrm{\Lambda }$. Our analysis reveals that the optimal energy range for detecting the $a_0(1817)$ meson lies between $W=3.4$ GeV and $W=3.6$ GeV, where the predicted total cross section reaches a minimum value of 112 nb. Notably, the $t$ channel, as predicted by the Regge model, significantly enhances the differential cross sections, particularly at extreme forward angles. Furthermore, we investigate the Dalitz processes of $2\to 3$ and discuss the feasibility of detecting the $a_0(1817)$ meson in experiments such as J-PARC.