Abreu, L. M., Song, J., Brandao, P. C. S., & Oset, E. (2024). A note on the tensor and vector exchange contributions to K (K)over-bar → K (K)over-bar, D(D)over-bar → D(D)over-bar and π+π- → π+π- reactions. Eur. Phys. J. A, 60(3), 76–10pp.
Abstract: In this note we study the tensor and vector exchange contributions to the elastic reactions involving the pseudoscalars mesons pi(+) pi(-), K+ K- and D+D-. In the case of the tensor-exchange contributions we assume that an intermediate tensor f(2)(1270) is dynamically generated from the interaction of two virtual rho mesons, with the use of a pole approximation. The calculation of the two-loop amplitude is facilitated since the triangle loops can be factorized and computed separately. The results show very small contributions coming from the tensor-exchange mechanisms when compared with those from the vector-exchange processes. We compare our results for pi pi and K (K) over bar scattering with those obtained in other works where the f2(1270) is considered as an ordinary q (q) over bar meson. Our picture provides a smaller contribution but of similar order of magnitude for pion scattering and stabilizes the results in the case of K (K) over bar, allowing us to make estimates for D (D) over bar scattering.
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Brandao, P. C. S., Song, J., Abreu, L. M., & Oset, E. (2023). B+ decay to K+ ηη with (ηη) from the D bar-D(3720) bound state. Phys. Rev. D, 108(5), 054004–6pp.
Abstract: We search for a B decay mode where one can find a peak for a DD bound state predicted in effective theories and in lattice QCD calculations, which has also been claimed from some reactions that show an accumulated strength in D D over bar production at threshold. We find a good candidate in the B+-> K+eta eta reaction, by looking at the eta eta mass distribution. The reaction proceeds via a first step in which one has the B+-> D*+ D-0 reaction followed by D*(+) (s) decay to (DK+)-K-0 and a posterior fusion of D-0 over bar D-0 to eta eta, implemented through a triangle diagram that allows the D-0 over bar D-0 to be virtual and to produce the bound state. The choice of eta eta to see the peak is based on results of calculations that find the eta eta among the light pseudoscalar channels with stronger coupling to the D D over bar bound state. We find a neat peak around the predicted mass of that state in the eta eta mass distribution, with an integrated branching ratio for B+-> K+ (D D, bound); (D D, bound) -> eta eta of the order of 1.5 x 10(-4), a large number for hadronic B decays, which should motivate its experimental search.
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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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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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Song, J., Dai, L. R., & Oset, E. (2022). How much is the compositeness of a bound state constrained by a and r(0)? The role of the interaction range. Eur. Phys. J. A, 58(7), 133–10pp.
Abstract: 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-s0* (2317) and D-s1* (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.
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Song, J., Feijoo, A., & Oset, E. (2022). Role of meson interactions in the D-s(+) -> pi(+) pi(+) pi(-) eta decay. Phys. Rev. D, 106(7), 074027–20pp.
Abstract: We perform a theoretical study of the D-s(+) ->pi(+)pi(+)pi(-)eta decay. We look first at the basic D-s(+) decay at the quark level from external and internal emission. Then we hadronize a pair or two pairs of q (q) over bar states to have mesons at the end. Posteriorly the pairs of mesons are allowed to undergo final state interaction, by means of which the a(0)(980), f(0)(980), a(1)(1260), and b(1)(1235) resonances are dynamically generated. The G parity is used as a filter of the possible channels, and from those with negative G parity only the ones that can lead to pi(+)pi(+)pi(-)eta at the final state are kept. Using transition amplitudes from the chiral unitary approach that generates these resonances and a few free parameters, we obtain a fair reproduction of the six mass distributions reported in the BESIII experiment.
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Wang, W. F., Feijoo, A., Song, J., & Oset, E. (2022). Molecular Omega(ce), Omega(bb), and Omega(bc) states. Phys. Rev. D, 106(11), 116004–14pp.
Abstract: We study the interaction of meson-baryon coupled channels carrying quantum numbers of a Omega(ce), Omega(bb), and Omega(bc) presently under investigation by the LHCb Collaboration. The interaction is obtained from an extension of the local hidden gauge approach to the heavy quark sector that has proved to provide accurate results compared to experiment in the case of Omega(c), Xi(c) states and pentaquarks, P-c and P-cs. We obtain many bound states, with small decay widths within the space of the chosen coupled channels. The spin-parity of the states are J(P) = 1/2(-) for coupled channels of pseudoscalar-baryon (1/2(+)), J(P) = 3/2(-) for the case of pseudoscalar-baryon (3/2(+)), J(P) = 1/2(-), 3/2(-) for the case of vector-baryon (1/2(+)) and J(P) = 1/2(-), 3/2(-). 5/2(-) for the vector- baryon (3/2(+)) channels. We look for poles of the states and evaluate the couplings to the different channels. The couplings obtained for the open channels can serve as a guide to see in which reaction the obtained states are more likely to be observed.
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