Dai, L. R., Abreu, L. M., Feijoo, A., & Oset, E. (2023). The isospin and compositeness of the Tcc(3875) state. Eur. Phys. J. C, 83(10), 983–11pp.
Abstract: We perform a fit to the LHCb data on the T-cc(3875) state in order to determine its nature. We use a general framework that allows to have the (DD & lowast;+)-D-0, (D+D & lowast;0) components forming a molecular state, as well as a possible nonmolecular state or contributions from missing coupled channels. From the fits to the data we conclude that the state observed is clearly of molecular nature from the (DD & lowast;+)-D-0, (D+D & lowast;0) components and the possible contribution of a nonmolecular state or missing channels is smaller than 3%, compatible with zero. We also determine that the state has isospin I=0 with a minor isospin breaking from the different masses of the channels involved, and the probabilities of the (DD & lowast;+)-D-0, (D+D & lowast;0) channels are of the order of 69% and 29% with uncertainties of 1%. The differences between these probabilities should not be interpreted as a measure of the isospin violation. Due to the short range of the strong interaction where the isospin is manifested, the isospin nature is provided by the couplings of the state found to the (DD & lowast;+)-D-0, (D+D & lowast;0) components, and our results for these couplings indicate that we have an I=0 state with a very small isospin breaking. We also find that the potential obtained provides a repulsive interaction in I=1, preventing the formation of an I=1 state, in agreement with what is observed in the experiment.
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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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Dai, L. R., & Oset, E. (2024). Dynamical generation of the scalar f0(500), f0(980), and K0*(700) resonances in the Ds+ → K+ π+ π- reaction. Phys. Rev. D, 109(5), 054008–9pp.
Abstract: We develop a model aimed at understanding the three mass distributions of pairs of mesons in the Cabibbo-suppressed D-s(+) – K+pi(+)pi(-) decay recently measured with high statistics by the BESIII collaboration. The largest contributions to the process come from the D-s(+) -> K+ rho(0) and D-s(+) -> K*(0)pi(+) decay modes, but the D-s(+) -> K-0*(1430)pi(+) and D-s(+) -> K+ f(0) (1370) modes also play a moderate role and all of them are introduced empirically. Instead, the contribution of the f(0)(500), f(0)(980) , and K-0*(700) resonances is introduced dynamically by looking at the decay modes at the quark level, hadronizing q (q) over bar over bar pairs to give two mesons, and allowing these mesons to interact, for which we follow the chiral unitary approach, to finally produce the K+ pi(+) pi(-) final state. While the general features of the mass distributions are fairly obtained, we pay special attention to the specific effects created by the light scalar resonances, which are visible in the low mass region of the pi(+) pi(-) (f(0)(500) and K+ pi(-) K+pi-(K-0*(700)) mass distributions and a narrow peak for pi(+) pi(-) distribution corresponding to f(0)(980) excitation. The contribution of these three resonances is generated by only one parameter. We see the agreement found in these regions as further support for the nature of the light scalar states as dynamically generated from the interaction of pseudoscalar mesons.
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Feijoo, A., Dai, L. R., Abreu, L. M., & Oset, E. (2024). Correlation function for the Tbb state: Determination of the binding, scattering lengths, effective ranges, and molecular probabilities. Phys. Rev. D, 109(1), 016014–8pp.
Abstract: We perform a study of the (B*+B0), (BB+)-B-*0 correlation functions using an extension of the local hidden gauge approach which provides the interaction from the exchange of light vector mesons and gives rise to a bound state of these components in I = 0 with a binding energy of about 21 MeV. After that, we face the inverse problem of determining the low energy observables, scattering length and effective range for each channel, the possible existence of a bound state, and, if found, the couplings of such a state to each (B*+B0), (BB+)-B-*0 component as well as the molecular probabilities of each of the channels. We use the bootstrap method to determine these magnitudes and find that, with errors in the correlation function typical of present experiments, we can determine all these magnitudes with acceptable precision. In addition, the size of the source function of the experiment from where the correlation functions are measured can be also determined with a high precision.
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Martinez Torres, A., Garzon, E. J., Oset, E., & Dai, L. R. (2011). Limits to the fixed center approximation to Faddeev equations: The case of the phi(2170). Phys. Rev. D, 83(11), 116002–9pp.
Abstract: The fixed center approximation to the Faddeev equations has been used lately with success in the study of bound systems of three hadrons. It is also important to set the limits of the approach in those problems to prevent proliferation of inaccurate predictions. In this paper, we study the case of the phi(2170), which has been described by means of Faddeev equations as a resonant state of phi and K (K) over bar, and show the problems derived from the use of the fixed center approximation in its study. At the same time, we also expose the limitations of an alternative approach recently proposed.
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