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Song, J., Dai, L. R., & Oset, E. (2023). Evolution of compact states to molecular ones with coupled channels: The case of the X(3872). Phys. Rev. D, 108(11), 114017–11pp.
Abstract: We study the molecular probability of the X(3872) in the D0 over bar D*0 and D+D*- channels in several scenarios. One of them assumes that the state is purely due to a genuine nonmolecular component. However, it gets unavoidably dressed by the meson components to the point that in the limit of zero binding of the D0 over bar D*0 component becomes purely molecular. Yet, the small but finite binding allows for a nonmolecular state when the bare mass of the genuine state approaches the D0 over bar D*0 threshold, but, in this case the system develops a small scattering length and a huge effective range for this channel in flagrant disagreement with present values of these magnitudes. Next we discuss the possibility to have hybrid states stemming from the combined effect of a genuine state and a reasonable direct interaction between the meson components, where we find cases in which the scattering length and effective range are still compatible with data, but even then the molecular probability is as big as 95%. Finally, we perform the calculations when the binding stems purely from the direct interaction between the meson-meson components. In summary we conclude, that while present data definitely rule out the possibility of a dominant nonmolecular component, the precise value of the molecular probability requires a more precise determination of the scattering length and effective range of the D0 over bar D*0 channel, as well as the measurement of these magnitudes for the D+D*- channel which have not been determined experimentally so far.
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Roca, L., Song, J., & Oset, E. (2024). Molecular pentaquarks with hidden charm and double strangeness. Phys. Rev. D, 109(9), 094005–8pp.
Abstract: We analyze theoretically the coupled-channel meson-baryon interaction with global flavor c<overline>cssn and c<overline>csss, where mesons are pseudoscalars or vectors, and baryons have JP = 1/2+ or 3/2+. The aim is to explore whether the nonlinear dynamics inherent in the unitarization process within coupled channels can dynamically generate double- and triple-strange pentaquark-type states (Pcss and Pcsss, respectively), for which there is no experimental evidence to date. We evaluate the s-wave scattering matrix by implementing unitarity in coupled channels, using potential kernels obtained from t-channel vector meson exchange. The required PPV and VVV vertices are obtained from Lagrangians derived through appropriate extensions of the local hidden gauge symmetry approach to the charm sector, while capitalizing on the symmetry of the spin and flavor wave function to evaluate the BBV vertex. We find four different poles in the double strange sector, some of them degenerate in spin. For the triple-strange channel, we find the meson-baryon interaction insufficient to generate a bound or resonance state through the unitary coupled-channel dynamics.
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Dai, L. R., Song, J., & Oset, E. (2023). Evolution of genuine states to molecular ones: The Tcc(3875) case. Phys. Lett. B, 846, 138200–6pp.
Abstract: We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the Tcc(3875) state, but are easily generalized to any hadronic system.
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