A Model of Baryons Made of Quarks with Hidden Spin

Abstract

The quark model of baryons is investigated in an attempt to combine its excellent agreement with experiment with a consistent foundation. It is found that effective Bose statistics for the spin states of identical quarks (quark statistics) is sufficient to explain the properties of baryons as if the three-quark wave functions were in the 56 representation of $\mathrm{SU}(6)$. A new internal degree of freedom is suggested as a mechanism for achieving quark statistics with fermion quarks. This mechanism also can produce quark saturation (at 3) and allows for the possibility of light quarks ($\ensuremath{\sim}\frac{1}{3}{M}_{p}$) that have a large effective mass if removed from baryons. Baryon magnetic moments and mass differences are analyzed in the quark model with the primary purpose of determining the required properties of quarks. Sum rules that are independent of quark moments in a static $s$-wave model are derived for baryon magnetic moments. Relativistic effects on magnetic moments are considered and are shown to be a likely mechanism for the deviation of the proton-neutron magnetic-moment ratio from the static prediction of $\ensuremath{-}\frac{3}{2}$. Higher-orbital states are also considered and a general formula is derived for orbital contributions to baryon magnetic moments.