HALL POST INEQUALITIES: review and application to molecules and tetraquarks

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.

44 pages, 15 figures, to appear in Annals of Physics

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Cited by in corpus (16)

• Spectrum of fully-heavy tetraquarks from a diquark+antidiquark perspective
• Masses of fully heavy tetraquarks $QQ\bar{Q}\bar{Q}$ in an extended relativized quark model
• Masses of doubly heavy tetraquarks $T_{Q{Q}^{\prime }}$ in a relativized quark model
• Masses of the $QQ\bar{Q}\bar{Q}$ tetraquarks in the relativistic diquark--antidiquark picture
• Double-heavy tetraquark states with heavy diquark-antiquark symmetry
• Open charm and bottom tetraquarks in an extended relativized quark model
• Fully-heavy tetraquark spectroscopy in the relativistic quark model
• Importance of meson-meson and of diquark-antidiquark creation operators for a $\bar{b}\bar{b}ud$ tetraquark
• Triply heavy tetraquark states
• Triply-heavy tetraquarks in an extended relativized quark model
• Doubly heavy tetraquark states in a mass splitting model
• Effect of relativistic kinematics on the stability of multiquarks
• Hadrons and Few-Body Physics
• Thermodynamics at zero temperature: inequalities for the ground state of a quantum many-body system
• Upper bounds for critical coupling constants for binding some quantum many-body systems
• Systematic study of fully heavy-flavored tetraquarks $Q_1{Q}_2{\bar{Q}}_1{\bar{Q}}_2(Q_{1;2}\in \left\{b;c\right\})$: Mass spectra, threshold analysis, and confrontation with LHC data