Pion, σ meson, and diquarks in the two-flavor color-superconducting phase of dense cold quark matter

The spectrum of meson and diquark excitations of dense cold quark matter is investigated in the framework of a Nambu--Jona-Lasinio type model for light quarks of two flavors. It was found out that a first order phase transition occurs when the chemical potential $\mu$ exceeds the critical value $\mu_c=350$ MeV. Above $\mu_c$, the diquark condensate $\vev{qq}$ forms, breaking the color symmetry of strong interaction. The masses of $\pi$- and $\sigma$-mesons are shown to grow with the chemical potential $\mu$ in the color-superconducting phase, but the mesons themselves become almost stable particles due to the Mott effect. Moreover, we have found in this phase an abnormal number of three, instead of five, Nambu--Goldstone bosons, together with a color doublet of light stable diquark modes and a color-singlet heavy diquark resonance with the mass $\sim$ 1100 MeV. In the color symmetric phase, \textit{i.e.} for $\mu <\mu_c$, the splitting between the masses of diquarks and antidiquarks is shown to arise if $\mu\ne 0$, contrary to the case of vanishing chemical potential, $\mu = 0$, where the mass spectrum of antidiquarks and diquarks is degenerate at the value $\sim$ 700 MeV.