Counting of oscillatory modes of valence quarks forming qqq baryons for 3 quark flavors u,d,s

¹ University of Nantes, Nantes, France
² Albert Einstein Center for Fundamental Physics - ITP, University of Bern, Bern, Switzerland

^a e-mail: kabana@mail.cern.ch
^b e-mail: mink@itp.unibe.ch

Published online: 5 December 2017

Abstract

We present a selection the unique properties of oscillatory modes of N _fl = 3 light quarks -u, d, s-, using the broken symmetry classification. stands for the space rotation group generated by the sum of the three individual angular momenta of quarks in their c.m. system. The baryonic multiplets are shown to emerge from the picture of oscillating quarks in 3 space dimensions in the center of mass system of the baryons. All oscillatory modes are fully relativistic with a finite number of oscillators and ths is forming the unique harmonic oscillators with these properties. The density of states as a function of mass-square is calculated. This estimate is of relevance for the accounting of the missing states of unobserved hadrons, as the here estimated baryonic 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.