Mesons and diquarks in a dense quark medium with color superconductivity

In the framework of the Nambu–Jona-Lasinio model with two quark flavors, we investigate the spectrum of meson and diquark excitations of dense quark matter in the phase with color superconductivity. The color $SU_{\mathrm{c}}(3)$ symmetry is spontaneously broken to $SU_{\mathrm{c}}(2)$ in this phase. But instead of the expected five Goldstone bosons in the mass spectrum, we observe only three, among which two bosons obey the quadratic dispersion law. We find the doublet of light diquark states with the mass $\sim15$ MeV and also the heavy diquark resonance $(SU_{\mathrm{c}}(2)$ singlet$)$ with the mass $\sim1100$ MeV. The $\pi$- and $\sigma$-mesons have the mass $\sim330$ Mev in the phase with color superconductivity. The $\pi$-mesons are then stable particles, while the $\sigma$-meson is stable only in the chiral limit in which the current quark mass $m_0$ becomes zero. If $m_0\ne0$, then the $\sigma$-meson mixes with diquarks in the phase with color superconductivity and becomes a resonance with the width $\sim30$ MeV.