Mass spectrum of diquarks and mesons in the color--flavor locked phase of dense quark matter

Abstract

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu -- Jona-Lasinio model with three types of massless quarks in the presense of a quark number chemical potential $\mu$. We investigate the effective action of meson- and diquark fields both at sufficiently large values of $\mu>\mu_c\approx 330$ MeV, where the color--flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter ($\mu<\mu_c$). In the last case all nine pseudoscalar mesons are Nambu -- Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400$\div$500 MeV for not too large values of $\mu>\mu_c$.