Mesons and diquarks in neutral color superconducting quark matter with \(\beta\)-equilibrium

Abstract

The spectrum of meson and diquark excitations in cold color-superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with \(\beta\)-equilibrium. A 2-flavored Nambu--Jona-Lasinio type model including a baryon \(\mu_B\), color \(\mu_8\), and electric \(\mu_Q\) chemical potentials is used. Two relations between coupling constants \(H\) and \(G\) in the diquark- and quark-antiquark channels, correspondingly, are treated, \(H=3G/4\) and \(H=G\). At \(H=3G/4\) the gapless- and at \(H=G\) the gapped neutral color superconductivity is realized. It is shown that color and electrical neutrality together with \(\beta\)-equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non--neutral matter. It is also shown that the properties of the physical \(SU(2)_c\)-singlet diquark excitation in the 2SC ground state varies for different parameterization schemes. Thus, for \(H=3G/4\) one finds a heavy resonance with mass \(\sim\) 1100 MeV in the non--neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass \(\sim\mu_Q\sim\) 200 MeV appears in the gapless 2SC phase. For \(H=G\), there is again a resonance (with the mass \(\sim\) 300 MeV) in the neutral gapped 2SC phase. Hence, the existence of the stable massive SU(2)\(_c\)-singlet diquark excitation is a new peculiarity of the gapless 2SC.