Abstract
In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons.
Highlights
The relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states
It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass
The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance
Summary
The relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. На этой основе выводится уравнение движения для двух частиц в релятивистской квантовой механике (РКМ) с лоренц-скалярным модифицированным потенциалом типа воронки. Для двух бесспиновых частиц с центральным потенциалом взаимодействия в системе центра инерции (СЦИ) оно имеет вид (ћ = c = 1) [26, 27]
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