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Search for the $D^{} \bar{D}^{}$ molecular state $X_{2} (4013)$ in $K^{-} p$ and $p p$ collisions

Min Yuan ¹, Bo Nan Zhang ², and Yin Huang ^1,*

¹School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
²College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot, 010022, China

^*Contact author: huangy2019@swjtu.edu.cn

Phys. Rev. D 113, 056002 – Published 5 March, 2026

DOI: https://doi.org/10.1103/h8vb-2hfy

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 $J^{P C} = 2^{+ +}$ . Its experimental confirmation, however, remains elusive. In this work, we investigate the production mechanisms of $X_{2} (4013)$ in the reactions $K^{-} p \to D_{s}^{-} Λ_{c}^{+} X_{2} (4013)$ and $p p \to Λ_{c}^{+} Λ_{c}^{+} X_{2} (4013)$ within an effective Lagrangian framework. The production processes are modeled via $t$ -channel $D^{*} / \bar{D}^{*}$ meson exchanges, while initial-state interactions (ISIs) 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 ISIs enhances the cross sections by nearly 1 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 $p p$ 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 ISIs in high-energy particle investigations.

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Phys. Rev. D 113, 056002– Published 5 March, 2026

Vol. 113, Iss. 5 — 1 March 2026

Received 16 October 2025
Accepted 6 February 2026

DOI: https://doi.org/10.1103/h8vb-2hfy

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Search for the $D^{} \bar{D}^{}$ molecular state $X_{2} (4013)$ in $K^{-} p$ and $p p$ collisions

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Search for the D*D¯ * molecular state X2(4013) in K−p and pp collisions

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Search for the $D^{} \bar{D}^{}$ molecular state $X_{2} (4013)$ in $K^{-} p$ and $p p$ collisions