Counting of oscillatory modes of valence quarks forming q–q̄ mesons

Abstract

We present the unique properties of oscillatory modes of valence quarks [Formula: see text] and antiquarks in mesons and the mass spectrum of associated mesons. The mesonic multiplets are shown to emerge from the picture of oscillating quarks and antiquarks in three space dimensions in the center of mass system of the mesons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of masssquare is calculated. Since it is known that there are missing states of unobserved hadrons this estimate is of relevance for the accounting of the latter, as the here estimated mesonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.