HALL POST INEQUALITIES: review and application to molecules and tetraquarks

TL;DR

This paper reviews Hall-Post inequalities that provide lower bounds for quantum system energies and explores their applications to molecules and tetraquarks, offering insights into exotic meson stability.

Contribution

It introduces new applications of Hall-Post inequalities to complex systems like molecules and tetraquarks, highlighting their utility in constraining bound states.

Findings

Hall-Post inequalities give lower bounds for ground-state energies.

Applications to molecules and tetraquarks constrain exotic meson stability.

Bounds are useful even when some subsystems lack bound states.

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.