Light- and heavy-quark symmetries and the \(Y(4230)\), \(Y(4360)\), \(Y(4500)\), \(Y(4620)\) and \(X(4630)\) resonances

• Published in: arXiv.org
• Main Authors: Fang-Zheng, Peng, Mao-Jun, Yan, Mario Sánchez Sánchez, Manuel Pavon Valderrama
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 05.01.2023
• Subjects: Charm (particle physics); Field theory; Flavor (particle physics); Mass distribution; P waves; Quarks
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2205.13590

The heavy hadron spectrum is constrained by symmetries, of which two of the most important ones are heavy-quark spin and SU(3)-flavor symmetries. Here we argue that in the molecular picture the \(Y(4230)\) (or \(Y(4260)\)), the \(Y(4360)\) and the recently discovered \(Y(4500)\) and \(Y(4620)\) vector-like resonances are linked by these two symmetries. By formulating a contact-range effective field theory for the \(D \bar{D}_1\) and \(D_s \bar{D}_{s1}\) family of S- and P-wave charmed meson-antimeson systems, we find that if the \(Y(4230)\) were to be a pure \(D \bar{D}_1\) molecular state, there would be a \(D^* \bar{D}_1\) partner with a mass similar to the \(Y(4360)\), a \(D_s \bar{D}_{s1}\) partner with a mass close to the \(Y(4500)\) and three \(J=1,2\) \(D_s^* \bar{D}_{s1}\) and \(J=3\) \(D_s^* \bar{D}_{s2}^{*}\) bound states with a mass in the vicinity of \(4630\,{\rm MeV}\), of which the first one (\(J=1\)) might correspond with the \(Y(4620)\). The previous predictions can in turn be improved by modifying the assumptions we have used to build the effective field theory. In particular, if we consider the closeness of the \(D^* \bar{D}_1\)-\(D^* \bar{D}_2^*\) and \(D_s^* \bar{D}_{s1}\)-\(D_s^* \bar{D}_{s2}^*\) thresholds and include the related coupled channel dynamics, we predict a \(J=2\) positive C-parity state with a mass around \(4650\,{\rm MeV}\). This hidden-strange and hidden-charm state might in turn be identified with the \(X(4630)\) that has been discovered past year by the LHCb in the \(J/\psi \phi\) invariant mass distribution.