Richard, J. M., Valcarce, A., & Vijande, J. (2020). Hall-Post inequalities: Review and application to molecules and tetraquarks. Ann. Phys., 412, 168009–32pp.
Abstract: A review is presented of the Hall-Post inequalities that give lower-bounds to the ground-state energy of quantum systems in terms of energies of smaller systems. New applications are given for systems experiencing both a static source and inner interactions, as well as for hydrogen-like molecules and for tetraquarks in some quark models. In the latter case, the Hall-Post inequalities constrain the possibility of deeply-bound exotic mesons below the threshold for dissociation into two quark-antiquark mesons. We also emphasize the usefulness of the Hall-Post bounds in terms of 3-body energies when some 2-body subsystems are ill defined or do not support any bound state.
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Garcilazo, H., Valcarce, A., & Vijande, J. (2020). Xi(-)t quasibound state instead of Lambda Lambda nn bound state. Chin. Phys. C, 44(2), 024102–7pp.
Abstract: The coupled Lambda Lambda nn – Xi-pnn system was studied to investigate whether the inclusion of channel coupling is able to bind the Lambda Lambda nn system. We use a separable potential three-body model of the coupled Lambda Lambda nn – Xi-pnn system and a variational four-body calculation with realistic interactions. Our results exclude the possibility of a bound state by a large margin. Instead, we found a Xi(-)t quasibound state above the Lambda Lambda nn threshold.
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Garcilazo, H., Valcarce, A., & Vijande, J. (2020). Neutral baryonic systems with strangeness. Int. J. Mod. Phys. E, 29(1), 1930009–22pp.
Abstract: We review the status as regards to the existence of three- and four-body bound states made of neutrons and Lambda hyperons. For interesting cases, the coupling to neutral baryonic systems made of charged particles of different strangeness has been addressed. There are strong arguments showing that the Lambda nn system has no bound states. Lambda Lambda nn strong stable states are not favored by our current knowledge of the strangeness -1 and -2 baryon-baryon interactions. However, a possible Xi(-) t quasibound state decaying to Lambda Lambda nn might exist in nature. Similarly, there is a broad agreement about the nonexistence of Lambda Lambda n bound states. However, the coupling to Xi NN states opens the door to a resonance above the Lambda Lambda n threshold.
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Richard, J. M., Valcarce, A., & Vijande, J. (2020). Very Heavy Flavored Dibaryons. Phys. Rev. Lett., 124(21), 212001–4pp.
Abstract: We explore the possibility of very heavy dibaryons with three charm quarks and three beauty quarks, bbbccc, using a constituent model which should lead to the correct solution in the limit of hadrons made of heavy quarks. The six-body problem is treated rigorously, in particular taking into account the orbital, color, and spin mixed-symmetry components of the wave function. Unlike a recent claim based on lattice QCD, no bound state is found below the lowest dissociation threshold.
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Richard, J. M., Valcarce, A., & Vijande, J. (2021). Effect of relativistic kinematics on the stability of multiquarks. Phys. Rev. D, 103(5), 054020–8pp.
Abstract: We discuss whether the bound nature of multiquark states in quark models could benefit from relativistic effects on the kinetic energy operator. For mesons and baryons, relativistic corrections to the kinetic energy lead to lower energies, and thus call for a retuning of the parameters of the model. For multiquark states, as well as their respective thresholds, a comparison is made of the results obtained with nonrelativistic and relativistic kinetic energy. It is found that the binding energy is lower in the relativistic case. In particular, QQ (q) over bar(q) over bar tetraquarks with double heavy flavor become stable for a larger ratio of the heavy to light quark masses; the all-heavy tetraquarks QQ (Q) over bar(Q) over bar that are not stable in standard nonrelativistic quark models remain unstable when a relativistic form of kinetic energy is adopted.
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Fernandez-Carames, T., Valcarce, A., & Vijande, J. (2010). Charged charmonium molecules. Phys. Rev. D, 82(5), 054032–5pp.
Abstract: We make use of a self-consistent quark-model based study of four-quark charmonium-like states to interpret recent charmonium experimental data. We conclude that there exists a D*(D) over bar* meson-meson molecule with quantum numbers (I-G) J(PC) = (1(-))2(++). Our study confirms the presence of charged charmonium-like resonances on the excited charmonium spectrum. We find support from recent experimental data by the Belle Collaboration [R. Mizuk et al. (Belle Collaboration), Phys. Rev. D 78, 072004 (2008)]. Confirmation of the experimental data by the Belle Collaboration and the determination of the quantum numbers of the new structures would help in discriminating among different theoretical models and would give further support to the theoretical analysis of T. Fernandez-Carames, A. Valcarce, and J. Vijande [Phys. Rev. Lett. 103, 222001 (2009)].
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Fernandez-Carames, T., Valcarce, A., & Vijande, J. (2011). Doubly charmed exotic mesons: A gift of nature? Phys. Lett. B, 699(4), 291–295.
Abstract: We study doubly charmed exotic states by solving the scattering problem of two D mesons. Our results point to the existence of a stable isoscalar doubly charmed meson with quantum numbers (I)J(P) = (0)1(+). We perform a thorough comparison to the results obtained within the hyperspherical harmonic formalism. Such exotic states could be measured at LHC and RHIC. Their experimental observation would, for the first time, confirm the contribution of multiquark structures to hadron spectroscopy.
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Carames, T. F., Valcarce, A., & Vijande, J. (2012). Too many X's, Y's and Z's? Phys. Lett. B, 709(4-5), 358–361.
Abstract: A large number of new states have been reported during the last few years in charmonium spectroscopy above the charmed meson production threshold. They have been called X's, Y's, and Z's. We reflect on the influence of thresholds on heavy meson spectroscopy comparing different flavor sectors and quantum numbers. The validity of a quark-model picture above open-flavor thresholds would severely restrict the number of channels that may lodge meson-meson molecules.
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Vijande, J., & Valcarce, A. (2014). Unraveling the pattern of the XYZ mesons. Phys. Lett. B, 736, 325–328.
Abstract: We present a plausible mechanism for the origin of the XYZ mesons in the heavy meson spectra within a standard quark-model picture. We discuss the conditions required for the existence of four-quark bound states or resonances contributing to the heavy meson spectra, being either compact or molecular. We concentrate on charmonium and bottomonium spectra, where several new states, difficult to understand as simple quark-antiquark pairs, have been reported by different experimental collaborations. The pivotal role played by entangled meson-meson thresholds is emphasized.
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Vijande, J., Valcarce, A., & Garcilazo, H. (2014). Heavy-baryon quark model picture from lattice QCD. Phys. Rev. D, 90(9), 094004–6pp.
Abstract: The ground state and excited spectra of baryons containing three identical heavy quarks, b or c, have been recently calculated in nonperturbative lattice QCD. The energy of positive and negative parity excitations has been determined with high precision. Lattice results constitute a unique opportunity to learn about the quark-confinement mechanism as well as elucidating our knowledge about the nature of the strong force. We analyze the nonperturbative lattice QCD results by means of heavy-quark static potentials derived using SU(3) lattice QCD. We make use of different numerical techniques for the three-body problem.
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