We introduce the spin-charge separation mechanism to the quark-lepton unification models which consider the lepton number as the fourth color. In certain finite-density systems, quarks and leptons are decomposed into spinons and chargons, which carry the spin and charge degrees of freedom respectively. Neutrinos can be related to the spinons with respect to the electric-charge and spin separation in the early universe or other circumstances. Some effective, probably universal couplings between the spinon sector and the chargon sector are derived and a phenomenological description for the chargon condensate is proposed. It is then demonstrated that the spinon current can induce vorticity in the chargon condensate, and spinon zero modes are trapped in the vortices, forming spinon-vortex bound states. In cosmology this configuration may lead to the emission of extremely high energy neutrinos when vortices split and reconnect.Keywords: massive neutrinos, spin-charge separation, quark-lepton unification
The fourth color and the haplon modelNeutrinos are one of the most important probes to the quark-lepton unification. It has been proposed forty years ago that the lepton number can be considered as the fourth "color" 1 in the frameworks based on the gauge group SU (2) L × SU (2) R × SU (4) c , and the gauge group SO(10) 2 , respectively. Right-handed neutrinos are introduced in both models. The descents from the SO(10) are through the SU (5) group or the SU (2) L × SU (2) R × SU (4) c group. In the latter case the usual color group SU (3) c is extended to the group SU (4) c and the leptons are interpreted as the fourth color column. Using the original notations in Ref.1 , the first two generations of fermions are written as(1) where (P, N , λ, χ) indicates valency and (a, b, c, d) indicates color degrees of freedom. In Ref.1 the matrices (1) are also written in a composite way, with the more arXiv:1503.09158v1 [hep-ph]