Constraint Dynamics and RQM Bound States

TL;DR

This paper develops a relativistic bound-state model for flavored mesons using constraint RQM, deriving a wave equation with position-dependent masses and calculating mass spectra with a new interpolating formula.

Contribution

It introduces a novel relativistic two-body wave equation with position-dependent masses within the constraint RQM framework for flavored mesons.

Findings

Derived a relativistic wave equation with position-dependent masses.

Obtained an interpolating complex-mass formula for eigenmasses.

Calculated mass spectra for leading-state flavored mesons.

Abstract

Flavored mesons containing quarks of unequal masses are studied. The appropriate tool is the Bethe-Salpeter formalism, but its inherent complexity leads to series of difficulties mostly related to the central role played in it by the relative time or energy. We consider bound states in the spirit of "Constraint Relativistic Quantum Mechanics (RQM)". Interaction of quarks is described by the funnel-type potential with the distant dependent strong coupling, $\alpha_s(r)$. Relativistic bound-state problem is formulated with the use of symmetries, energy-momentum conservation laws in Minkowskiy space. Relativistic two-body wave equation with position dependent particle masses is derived and used to describe the flavored mesons. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Solution of the equation for the system in the form of a~standing wave is given. Interpolating complex-mass formula for two exact asymptotic eigenmass expressions is obtained. Mass spectra for some leading-state flavored mesons are calculated.