Probing the \(X(6900)\) via Two-photon Production in Ultraperipheral Collisions

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Studies of the internal structure of hadrons have been a main focus in particle physics since perturbative Quantum Chromodynamics (p-QCD) was established as the theory of the strong interaction. While the constituent quark model provided a successful framework for the investigation of many hadrons, recent decades have unveiled exotic states that defy simple classification. An example is the \(X(6900)\) resonance, identified in the di-\(J/\psi \) mass spectrum by LHCb, ATLAS, and CMS. As a tetraquark composed of \(c\bar {c}c\bar {c}\), its existence confirms the possibility of such multi-quark states. Its fundamental nature — whether it is a compact diquark–antidiquark entity or a diffuse molecule of two charmonia — remains an open question. We propose a study for the exclusive \(\gamma \gamma \to X(6900)\) process, accessible in ultraperipheral heavy-ion collisions (UPCs), which serves as a clean probe to differentiate between these inner structures. In this work, we calculate the respective two-photon decay width, \({\mit \Gamma }_{\gamma \gamma }\), using a leading-order Non-Relativistic QCD (NRQCD) framework. The long-distance matrix elements are determined from the wave functions at origin obtained in an extended relativized quark model. For the \(X(6900)\) as a radially excited (\(2s\)) compact state, we predict sizable widths of \({\mit \Gamma }_{\gamma \gamma }(2^{++}_{2s}) \approx 0.22\) keV and \({\mit \Gamma }_{\gamma \gamma }(0^{++}_{2s}) \approx 0.15\)–0.69 keV. These values are significantly larger than expected for a molecular state, providing a clear experimental discriminant. Abstract Published by the Jagiellonian University 2026 authors

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