Search for the $D^{*}\bar{D}^{*}$ Molecular State $X_{2}(4013)$ in $K^{-}p$ and $pp$ Collisions

TL;DR

This work addresses the search for the $X_2(4013)$, a $D^* \bar{D}^*$ molecular state with $J^{PC}=2^{++}$ predicted as the heavy-quark spin symmetry partner of $X(3872)$. It employs an effective Lagrangian framework to model production in $K^- p$ and $pp$ collisions, focusing on central production via $t$-channel exchanges and incorporating initial-state interactions through Pomeron and Reggeon exchanges. The study finds total cross sections at the pb level and shows that ISI enhances the rates by nearly an order of magnitude, with distinct angular signatures: forward-peaked in the $K^- p$ channel and a central dip in the $pp$ channel due to helicity dynamics and Pauli effects. These results provide concrete benchmarks for upcoming experimental searches at facilities like AMBER at CERN and LHCb, and underscore the importance of ISI in heavy-quark molecular state production.

Abstract

Motivated by the interpretation of $X(3872)$ as a $D\bar{D}^{*}$ molecular state, heavy-quark spin symmetry predicts a spin-2 partner, $X_{2}(4013)$, which can be regarded as a $D^{*}\bar{D}^{*}$ 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 $K^{-}p \to Λ_{c}^{+} D_{s}^{-} X_{2}(4013)$ and $pp \to Λ_{c}^{+}Λ_{c}^{+} X_{2}(4013)$ within an effective Lagrangian framework. The production processes are modeled via $t$-channel $D/\bar{D}^{*}$ 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.

Figures (5)

• Figure 1: Tree-level Feynman diagrams for $X_2(4013)$ production in the $K^- p \to D_s^- \Lambda_c^+ X_2(4013)$ and $pp \to \Lambda_c^+ \Lambda_c^+ X_2(4013)$ reactions. These processes proceed via the exchange of $D^*$ and $\bar{D}^*$ mesons. The grey-shaded region indicates initial-state interactions (ISI). Particle momenta $(p_1, p_2, p_3, p_4, q_1, q_2)$ are indicated.
• Figure 2: Initial-state interaction (ISI) mechanisms for the reactions $K^{-}p \to K^{-}p$ and $pp \to pp$.
• Figure 3: The total cross sections for the $K^-p\rightarrow D_s^-\Lambda_c^+X_2(4013)$ and $pp\rightarrow \Lambda_c^+\Lambda_c^+X_2(4013)$ reactions are evaluated for different $\alpha$ values.
• Figure 4: The cross section with and without ISI for the $K^-p\rightarrow D_s^-\Lambda_c^+X_2(4013)$ and $pp\rightarrow \Lambda_c^+\Lambda_c^+X_2(4013)$ reactions with $\alpha=1.7$.
• Figure 5: Differential cross sections for (a) $K^-p\rightarrow D_s^-\Lambda_c^+X_2(4013)$ (with ISI), (b) $np\rightarrow \Lambda_c^+ \Sigma_c(2445) X_2(4013)$, and (c)(d) $pp\rightarrow \Lambda_c^+\Lambda_c^+X_2(4013)$ (with and without ISI, respectively), calculated with $\alpha=1.7$. The black solid lines, red dashed lines, and blue dashed-dotted lines are obtained at beam energies $P=20$, 30, and 40 GeV, respectively.