Mesons and diquarks in neutral color superconducting quark matter with β equilibrium

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 two-flavored Nambu-Jona-Lasinio-type model including baryon mu(B), color mu(8), and electric mu(Q) chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the beta equilibrium. The sensitivity of the model to the tuning of the interaction constants in the diquark (H) and quark-antiquark (G) channels is examined for two different parametrization schemes by choosing the ratio H/G to be 3/4 and 1, respectively. The gapless neutral color superconductivity is realized at H=3G/4, and the gapped neutral color superconductivity at H=G. 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. The pi- and sigma-meson masses are evaluated to be similar to 300 MeV. It is also shown that the properties of the physical SU(2)(c)-singlet diquark excitation in the 2SC ground state vary for different parametrization schemes. Thus, for H=3G/4 one finds a heavy resonance with mass similar to 1100 MeV in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass similar to vertical bar mu(Q)vertical bar similar to 200 MeV appears in the gapless 2SC environment. For a stronger attraction in the diquark channel (H=G), there is again a resonance (with the mass similar to 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. In addition, the behavior of the diquark mass in vacuum, i.e., at mu(B)=0, as a function of H has been investigated.