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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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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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Dias, J. M., Debastiani, V. R., Roca, L., Sakai, S., & Oset, E. (2017). Binding of the BD(D)over-bar and BDD systems. Phys. Rev. D, 96(9), 094007–6pp.
Abstract: We study theoretically the BD (D) over bar and BDD systems to see if they allow for possible bound or resonant states. The three-body interaction is evaluated implementing the fixed center approximation to the Faddeev equations which considers the interaction of a D or (D) over bar particle with the components of a BD cluster, previously proved to form a bound state. We find an I(J(P)) = 1/2(0(-)) bound state for the BD (D) over bar system at an energy around 8925-8985 MeV within uncertainties, which would correspond to a bottom hidden-charm meson. In contrast, for the BDD system, which would be bottom double-charm and hence manifestly exotic, we have found hints of a bound state in the energy region 8935-8985 MeV, but the results are not stable under the uncertainties of the model, and we cannot assure, nor rule out, the possibility of a BDD three-body state.
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Debastiani, V. R., Sakai, S., & Oset, E. (2019). Considerations on the Schmid theorem for triangle singularities. Eur. Phys. J. C, 79(1), 69–13pp.
Abstract: We investigate the Schmid theorem, which states that if one has a tree level mechanism with a particle decaying to two particles and one of them decaying posteriorly to two other particles, the possible triangle singularity developed by the mechanism of elastic rescattering of two of the three decay particles does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced in the first decay and determine the limits of validity and violation of the theorem. One of the conclusions is that the theorem holds in the strict limit of zero width of that resonance, in which case the strength of the triangle diagram becomes negligible compared to the tree level. Another conclusion, on the practical side, is that for realistic values of the width, the triangle singularity can provide a strength comparable or even bigger than the tree level, which indicates that invoking the Schmid theorem to neglect the triangle diagram stemming from elastic rescattering of the tree level should not be done. Even then, we observe that the realistic case keeps some memory of the Schmid theorem, which is visible in a peculiar interference pattern with the tree level.
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Yu, Q. X., Pavao, R., Debastiani, V. R., & Oset, E. (2019). Description of the Xic and Xib states as molecular states. Eur. Phys. J. C, 79(2), 167–14pp.
Abstract: In this work we study several c and b states dynamically generated from the meson-baryon interaction in coupled channels, using an extension of the local hidden gauge approach in the Bethe-Salpeter equation. These molecular states appear as poles of the scattering amplitudes, and several of them can be identified with the experimentally observed c states, including the c(2790), c(2930), c(2970), c(3055) and c(3080). Also, for the recently reported b(6227) state, we find two poles with masses and widths remarkably close to the experimental data, for both the JP=1/2- and JP=3/2- sectors.
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