Mesons and diquarks in neutral color superconducting quark matter with β 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 β equilibrium. A two-flavored Nambu-Jona-Lasinio–type model including baryon μB, color μ8, and electric μQ chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the β 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 β 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 π- and σ-meson masses are evaluated to be ∼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 ∼1100 MeV in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass ∼|μQ|∼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 ∼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 μB=0, as a function of H has been investigated.

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