Mesons and diquarks in the color neutral 2SC phase of dense cold quark matter

Abstract

The spectrum of meson and diquark excitations of dense color neutral cold quark matter is investigated in the framework of a 2-flavored Nambu--Jona-Lasinio type model, including a quark $\mu$- and color ${\mu }_8$ chemical potential. It was found out that in the color superconducting (2SC) phase, i.e. at $\mu >{\mu }_c=342$ MeV, ${\mu }_8$ aquires rather small values $\sim$ 10 MeV in order to ensure the color neutrality. In this phase the $\pi$- and $\sigma$ meson masses are evaluated around $\sim$ 330 MeV. The spectrum of scalar diquarks in the color neutral 2SC phase consists of a heavy ($\mathrm{S}{\mathrm{U}}_{\mathrm{c}}(2)$-singlet) resonance with mass $\sim$ 1100 MeV, four light diquarks with mass $3|{\mu }_8|$, and one Nambu --Goldstone boson which is in accordance with the Goldstone theorem. Moreover, in the 2SC phase there are five light stable particles as well as a heavy resonance in the spectrum of pseudo-scalar diquarks. In the color symmetric phase, i.e. for $\mu <{\mu }_c$, a mass splitting of scalar diquarks and antidiquarks is shown to arise if $\mu \ne 0$, contrary to the case of $\mu =0$, where the masses of scalar antidiquarks and diquarks are degenerate at the value $\sim$~700 MeV. If the coupling strength in the pseudo-scalar diquark channel is the same as in the scalar diquark one (as for QCD-inspired NJL models), then in the color symmetric phase pseudo-scalar diquarks are not allowed to exist as stable particles.

Comments: 18 pages, 4 figures; version accepted for the publication in PRD