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Evaluating Alternative Spin Scenarios of \(P_{c\bar{c}}(4440)\) and \(P_{c\bar{c}}(4457)\) Using Heavy Quark Symmetries

  • Duygu Yıldırım

摘要

Heavy quark symmetries are useful for predicting the existence of heavy states, their masses, and spin states. Despite numerous studies on the \(P_{c\bar{c}}(4440)\) P c c ¯ ( 4440 ) and \(P_{c\bar{c}}(4457)\) P c c ¯ ( 4457 ) heavy states, their spin states have not been previously determined. In this study, heavy symmetries are applied to predict the spin states. If the \(P_{c\bar{c}}(4440)\) P c c ¯ ( 4440 ) and \(P_{c\bar{c}}(4457)\) P c c ¯ ( 4457 ) states are considered \(\bar{D}^*\Sigma _c\) D ¯ Σ c molecules, they can be classified as heavy partners. This classification may help clarify their potential connections with heavy antiquark-diquark symmetry partners. By utilizing these alternative spin assignments and the concept of heavy antiquark-diquark symmetry, it may be possible to estimate \(\Xi _{cc}^{(*)}\Sigma _c^{(*)}\) Ξ cc ( ) Σ c ( ) states, and ultimately, their spin states, which have not been elucidated in experiments. In addition to these symmetries, the relationship between \(P_{c\bar{c}}\) P c c ¯ and \(P_{c\bar{c}s}\) P c c ¯ s pentaquarks can be constructed which supports the prediction of possible \(P_{c\bar{c}s}\) P c c ¯ s states. The predicted masses of the \(P_{c\bar{c}s}(4338)\) P c c ¯ s ( 4338 ) and \(P_{c\bar{c}s}(4459)\) P c c ¯ s ( 4459 ) states align with several studies, allowing us to eliminate a specific spin state. One spin state appears to be favored, suggesting that \(P_{c\bar{c}}(4440)\) P c c ¯ ( 4440 ) has \(J^P=\frac{1}{2}\) J P = 1 2 and \(P_{c\bar{c}}(4457)\) P c c ¯ ( 4457 ) has \(J^P=\frac{3}{2}\) J P = 3 2 .