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Bayar, M., & Debastiani, V. R. (2017). a(0)(980) – f(0)(980) mixing in chi(c1) -> pi(0)f(0)(980) -> pi(0)pi(+)pi(-) and chi(c1) -> pi(0) a(0)(980) -> pi(0)pi(0)eta. Phys. Lett. B, 775, 94–99.
Abstract: We study the isospin breaking in the reactions chi(c1) -> pi(0)pi(+)pi(-) and chi(c1) -> pi(0)pi(0)eta and its relation to the a(0)(980) – f(0)(980) mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the chi(c1) -> eta pi(+)pi(-) reaction (also measured by BESIII), and further explored in the predictions to the eta(c) -> eta pi(+)pi(-), can be successfully employed in the present study. We assume that the chi(c1) behaves as an SU(3) singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the a(0)(980) and f(0)(980) are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of pairs of mesons created in the chi(c1) decay, or in the propagators inside the T matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the T matrix makes the pi(0)eta -> pi(+)pi(-) amplitude nonzero, which gives an important contribution and also enhances the effect of the K (K) over bar term. We also find that the most important effect in the total amplitude is the isospin breaking inside the T matrix, due to the constructive sum of pi(0)eta -> pi(+)pi(-) and K (K) over bar -> pi(+)pi(-), which is essential to get a good agreement with the experimental measurement of the mixing.
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Debastiani, V. R., & Navarra, F. S. (2019). A non-relativistic model for the [cc][(c)over-bar(c)over-bar] tetraquark. Chin. Phys. C, 43(1), 013105–20pp.
Abstract: We use a non-relativistic model to study the spectroscopy of a tetraquark composed of [cc][(c) over bar(c) over bar] in a diquark-antidiquark configuration. By numerically solving the Schrodinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the c (c) over bar spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite the heavy diquark mass, and also that the diquark has a finite size if treated in the same way as the c (c) over bar systems. We find that the lowest S-wave T-4c tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds. Finally, we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks. This might be relevant to the study of exotic charmonium in the quark-gluon plasma. The T4c states could be investigated in the forthcoming experiments at the LHC and Belle II.
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Debastiani, V. R., Liang, W. H., Xie, J. J., & Oset, E. (2017). Predictions for eta(c) -> eta pi(+)pi(-) producing f(0)(500), f(0)(980) and a(0)(980). Phys. Lett. B, 766, 59–64.
Abstract: We perform calculations for the eta(c) -> eta pi(+)pi(-) decay using elements of SU(3) symmetry to see the weight of different trios of pseudoscalars produced in this decay, prior to the final state interaction of the mesons. After that, the interaction of pairs of mesons, leading finally to eta pi(+)pi(-), is done using the chiral unitary approach. We evaluate the pi(+)pi(-) and pi eta mass distributions and find large and clear signals for f(0)(500), f(0)(980) and a(0)(980) excitation. The reaction is similar to the chi(c1) -> eta pi(+)pi(-), which has been recently measured at BESIII and its implementation and comparison with these predictions will be very valuable to shed light on the nature of the low mass scalar mesons.
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Ji, T., Dong, X. K., Albaladejo, M., Du, M. L., Guo, F. K., Nieves, J., et al. (2023). Understanding the 0(++) and 2(++) charmonium(-like) states near 3.9 GeV. Sci. Bull., 68(7), 688–697.
Abstract: We propose that the X(3915) observed in the J/psi x channel is the same state as the chi(c2)(3930), and the X(3960), observed in the Ds+Ds- channel, is an S-wave Ds+Ds- hadronic molecule. In addition, the J(PC) = 0(++) component in the B+ -> D+D-K+ assigned to the X(3915) in the current Review of Particle Physics has the same origin as the X(3960), which has a mass around 3.94 GeV. To check the proposal, the available data in the D (D) over bar and Ds+Ds- channels from both B decays and gamma gamma fusion reaction are analyzed considering both the D (D) over bar -D-s(D) over bar (s)-D*(D) over bar*-D-s*(D) over bar (s)* coupled channels with 0(++) and a 2(++) state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23 GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons.
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