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

References in corpus (2)

• Stability of asymmetric tetraquarks in the minimal-path linear potential
• Semirelativistic stability of N-boson systems bound by 1/r pair potentials

Cited by in corpus (8)

• Masses of doubly heavy tetraquarks $T_{Q{Q}^{\prime }}$ in a relativized quark model
• Fully-heavy tetraquark spectroscopy in the relativistic quark model
• 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
• 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
• Upper bounds for critical coupling constants for binding some quantum many-body systems