Richard, J. M., Valcarce, A., & Vijande, J. (2017). String dynamics and metastability of all-heavy tetraquarks. Phys. Rev. D, 95(5), 054019–7pp.
Abstract: Multiquark states have been advocated to explain recent experimental data in the heavy-light sector, and there are already speculations about multiquarks containing only heavy quarks and antiquarks. With a rigorous treatment of the four-body problem in current quark models, full-charm (cc (c) over bar(c) over bar) and full-beauty(bb (b) over bar(b) over bar) tetraquarks are found to be unbound. Thus their stability should rely on more subtle effects that are not included in the simple picture of constituent quarks. The case of (bc (b) over bar(c) over bar) might be more favorable if the naive color-additive model of confinement is replaced by a string-inspired interaction.
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Richard, J. M., Valcarce, A., & Vijande, J. (2017). Stable heavy pentaquarks in constituent models. Phys. Lett. B, 774, 710–714.
Abstract: It is shown that standard constituent quark models produce ((c)over-barcqqq) hidden-charm pentaquarks, where c denotes the charmed quark and q a light quark, which lie below the lowest threshold for spontaneous dissociation and thus are stable in the limit where the internal (c)over-barc annihilation is neglected. The binding is a cooperative effect of the chromoelectric and chromomagnetic components of the interaction, and it disappears in the static limit with a pure chromoelectric potential. Their wave function contains color sextet and color octet configurations for the subsystems and can hardly be reduced to a molecular state made of two interacting hadrons. These pentaquark states could be searched for in the experiments having discovered or confirmed the hidden-charm meson and baryon resonances.
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Richard, J. M., Valcarce, A., & Vijande, J. (2018). Few-body quark dynamics for doubly heavy baryons and tetraquarks. Phys. Rev. C, 97(3), 035211–10pp.
Abstract: We discuss the adequate treatment of the three- and four-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be somewhat misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.
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Richard, J. M., Valcarce, A., & Vijande, J. (2019). Pentaquarks with anticharm or beauty revisited. Phys. Lett. B, 790, 248–250.
Abstract: We use a constituent model to analyze the stability of pentaquark (Q) over bar qqqq configurations with a heavy antiquark (c) over bar or (b) over bar, and four light quarks uuds, ddsu or ssud. The interplay between chromoelectric and chromomagnetic effects is not favorable, and, as a consequence, no bound state is found below the lowest dissociation threshold.
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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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