Searching for the $G(3900)$ via the $K^- p \to D_s^- \Lambda_c^+ G(3900)^0$ reaction

Abstract

The nature of the $G(3900)$ structure, observed in $e^{+}e^{-}\to D\bar{D}$, remains unclear and may stem either from a genuine resonance or from charmonium interference and threshold effects. We therefore propose searching for the $G(3900)$ signal in the reaction $K^- p \to D_s^- \Lambda_c^+ G(3900)^0$, where the interference effects present in $e^{+}e^{-}\to \bar{D}^{*}D$ are absent. We employ an effective Lagrangian approach, where the reaction proceeds via a central production mechanism dominated by $t$-channel $D^{0}$ and $D^{*0}$ exchanges, based on the possible interpretation of $G(3900)$ as a $P$-wave $\bar{D}^{*}D$ molecular state, whose coupling to the $\bar{D}^{*}D$ channel is fixed from our previous fit to the $e^{+}e^{-}\to \bar{D}^{*}D$ data. The $\bar{K}N$ initial-state interaction, mediated by Pomeron and Reggeon exchanges, is also included and leads to a significant enhancement of the production cross section. If measured in future experiments, the predicted total cross sections and angular distributions can provide a promising probe of the nature of the $G(3900)$, and in particular of its possible genuine resonance nature.