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We evaluate theoretically the interaction of the open bottom and strange systems B¯K¯, B¯∗K¯, B¯K¯∗ and B¯∗K¯∗ to look for possible bound states which could correspond to exotic non-quark–antiquark mesons since they would contain at least one b and one s quarks. The s-wave scattering matrix is evaluated implementing unitarity by means of the Bethe–Salpeter equation, with the potential kernels obtained from contact and vector meson exchange mechanisms. The vertices needed are supplied from Lagrangians derived from suitable extensions of the hidden gauge symmetry approach to the bottom sector. We find poles below the respective thresholds for isospin 0 interaction and evaluate the widths of the different obtained states by including the main sources of imaginary part, which are the B∗→Bγ decay in the B¯∗K¯ channels, the K∗→Kπ in the channels involving a K∗, plus the box diagrams with B¯K¯ and B¯∗K¯ intermediate states for the B¯∗K¯∗ channels.

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 D 0 D ∗ + , D + D ∗ 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 D 0 D ∗ + , D + D ∗ 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 D 0 D ∗ + , D + D ∗ 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 D 0 D ∗ + , D + D ∗ 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.

We have conducted a model independent analysis of the K + K ¯ 0 pair correlation function obtained from ultra high energy pp collisions, with the aim of extracting the information encoded in it related to the K K ¯ interaction and the coupled channel π + η . With the present large errors at small relative K + K ¯ 0 momenta, we find that the information obtained about the scattering matrix suffers from large uncertainties. Even then, we are able to show that the data imply the existence of the a 0 resonance, a 0 ( 980 ) , showing as a strong cusp close to the K K ¯ threshold. We also mention that the measurement of the π + η correlation function will be essential in order to constrain more the information on K K ¯ dynamics that can be obtained from correlation functions.

We present an approach that allows one to obtain information on the compositeness of molecular states from combined information of the scattering length of the hadronic components, the effective range, and the binding energy. We consider explicitly the range of the interaction in the formalism and show it to be extremely important to improve on the formula of Weinberg obtained in the limit of very small binding and zero range interaction. The method allows obtaining good information also in cases where the binding is not small. We explicitly apply it to the case of the deuteron and the D s 0 ∗ ( 2317 ) and D s 1 ∗ ( 2460 ) states and determine simultaneously the value of the compositeness within a certain range, as well as get qualitative information on the range of the interaction.

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.

We have identified the decay modes of the Ds+→π+K∗+K∗-,π+K∗0K¯∗0 reactions producing a pion and two vector mesons. The posterior vector–vector interaction generates two resonances that we associate to the f0(1710) and the a0(1710) recently claimed, and they decay to the observed K+K- or KS0KS0 pair, leading to the reactions Ds+→π+K+K-,π+KS0KS0. The results depend on two parameters related to external and internal emission. We determine a narrow region of the parameters consistent with the large Nc limit within uncertainties which gives rise to decay widths in agreement with experiment. With this scenario we make predictions for the branching ratio of the a0(1710) contribution to the Ds+→π0K+KS0 reaction, finding values within the range of (1.3±0.4)×10-3. Comparison of these predictions with coming experimental results on that latter reaction will be most useful to deepen our understanding on the nature of these two resonances.

In this work we investigate the possibility of the formation of states from the dynamics involved in the D ∗ D ∗ D ∗ system by considering that two D ∗ ’s generate a J P = 1 + bound state, with isospin 0, which has been predicted in an earlier theoretical work. We solve the Faddeev equations for this system within the fixed center approximation and find the existence of J P = 0 - , 1 - and 2 - states with charm 3, isospin 1/2, masses ∼ 6000  MeV, which are manifestly exotic hadrons, i.e., with a multiquark inner structure.

We study the experimental DK invariant mass spectra of the reactions , B 0 → D - D 0 K + (measured by the BaBar collaboration) and B s → π + D ¯ 0 K - (measured by the LHCb collaboration), where an enhancement right above the threshold is seen. We show that this enhancement is due to the presence of D s 0 ∗ ( 2317 ) , which is a DK bound state in the I ( J P ) = 0 ( 0 + ) sector. We employ a unitarized amplitude with an interaction potential fixed by heavy meson chiral perturbation theory. We obtain a mass M D s 0 ∗ = 2315 - 17 + 12 - 5 + 10 MeV , and we also show, by means of the Weinberg compositeness condition, that the DK component in the wave function of this state is P D K = 70 - 6 + 4 - 8 + 4 % , where the first (second) error is statistical (systematic).

We study the [Formula omitted] reactions with [Formula omitted] and [Formula omitted], in the region of [Formula omitted] invariant masses of [Formula omitted] MeV. The strong coupling of the [Formula omitted] resonance to [Formula omitted] makes the mechanism based on [Formula omitted] exchange very efficient to produce this resonance observed in the [Formula omitted] invariant mass distribution. In addition, in all these reactions one observes an associated peak at 1420 MeV which comes from the [Formula omitted] decay mode of the [Formula omitted] when the [Formula omitted] is placed on shell at higher invariant masses. We call the attention to the possibility that the peaks observed in other reactions where the \" [Formula omitted]\" is observed have a similar origin.