Symmetry analysis of compact tetraquark states and implications for the fully charm candidates X (6600), X (6900), and X (7100)

Motivated by recent experimental observations, we investigate the J P distribution of low-energy compact tetraquark states using symmetry analysis based on inherent nodal structures. Assuming tetrahedral and square configurations for the qqq̅q̅ system, we derive the allowed orbital structures from the restricted representations of S 4 onto S 2 × S 2 for L ≤3. The accessible-state distribution is particularly prominent in the J P =2 + , 2 - , and 1 + sectors, with the 2 + sector showing the strongest low-energy preference. We further find that the symmetry-driven distribution is qualitatively similar to that of the three-flavor four-quark system, and that the dominant J P =2 + pattern persists under phenomenological weightings inspired by chromomagnetic interaction (CMI) considerations. These results suggest that the low-lying compact tetraquark spectrum is primarily constrained by symmetry, while the detailed distribution exhibits sensitivity to dynamical weightings. Applying this framework to the fully charm candidates X (6600), X (6900), and X (7100), we find that their observed J PC =2 ++ quantum numbers are consistent with a low-lying compact tetraquark interpretation. The relative ordering of the 1 - and 1 + states is found to be particularly sensitive to the phenomenological weighting, suggesting a direction for future investigation with more rigorous methods. Furthermore, the 2 - and 1 + channels emerge as potential subleading candidates after 2 + , providing useful targets for future experimental searches. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.