Search for the $D^{\ast }{\bar{D}}^{\ast }$ Molecular State $X_2(4013)$ in $K^{-}p$ and $pp$ Collisions

Abstract

Motivated by the interpretation of $X(3872)$ as a $D{\bar{D}}^{\ast }$ molecular state, heavy-quark spin symmetry predicts a spin-2 partner, $X_2(4013)$, which can be regarded as a $D^{\ast }{\bar{D}}^{\ast }$ molecule with quantum numbers $J^{PC}=2^{++}$. Its experimental confirmation, however, remains elusive. In this work, we investigate the production mechanisms of $X_2(4013)$ in the reactions $K^{-}p\to {\Lambda }_c^{+}{D}_s^{-}{X}_2(4013)$ and $pp\to {\Lambda }_c^{+}{\Lambda }_c^{+}{X}_2(4013)$ within an effective Lagrangian framework. The production processes are modeled via $t$-channel $D/{\bar{D}}^{\ast }$ meson exchanges, while initial-state interactions (ISI) mediated by Pomeron and Reggeon exchanges are also taken into account. Our calculations indicate that the total cross sections can reach the pb level, suggesting that $X_2(4013)$ may be accessible at current and future experiments such as AMBER@CERN and LHCb. Inclusion of ISI enhances the cross sections by nearly one order of magnitude. The differential distributions show distinct angular behaviors for the two reactions: the $K^{-}p$ reaction exhibits a forward-peaked distribution, whereas the $pp$ reaction shows a dip near central angles. This study provides a quantitative theoretical benchmark for future experimental searches of $X_2(4013)$ and highlights the importance of initial-state interactions (ISI) in high-energy particle investigations.

Comments: 6 pages, 5 figures, 1 table