Mesons and diquarks in the color neutral superconducting 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 two-flavored Nambu--Jona-Lasinio--type model, including a quark $\ensuremath{\mu}$- and color ${\ensuremath{\mu}}_{8}$-chemical potential. It was found that, in the color superconducting (2SC) phase, i.e. at $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}=342\text{ }\text{ }\mathrm{MeV}$, ${\ensuremath{\mu}}_{8}$ acquires rather small values $\ensuremath{\sim}10\text{ }\text{ }\mathrm{MeV}$ in order to ensure the color neutrality. In this phase the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ meson masses are evaluated around $\ensuremath{\sim}330\text{ }\text{ }\mathrm{MeV}$. The spectrum of scalar diquarks in the color neutral 2SC phase consists of a heavy [${\mathrm{SU}}_{c}(2)$-singlet] resonance with mass $\ensuremath{\sim}1100\text{ }\text{ }\mathrm{MeV}$, four light diquarks with mass $3|{\ensuremath{\mu}}_{8}|$, 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 pseudoscalar diquarks. In the color symmetric phase, i.e. for $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, a mass splitting of scalar diquarks and antidiquarks is shown to arise if $\ensuremath{\mu}\ensuremath{\ne}0$, contrary to the case of $\ensuremath{\mu}=0$, where the masses of scalar antidiquarks and diquarks are degenerate at the value $\ensuremath{\sim}700\text{ }\text{ }\mathrm{MeV}$. If the coupling strength in the pseudoscalar diquark channel is the same as in the scalar diquark one (as for QCD-inspired Nambu--Jona-Lasinio models), then in the color symmetric phase pseudoscalar diquarks are not allowed to exist as stable particles.