Mesons and diquarks in neutral color superconducting quark matter withβequilibrium

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 $\ensuremath{\beta}$ equilibrium. A two-flavored Nambu-Jona-Lasinio--type model including baryon ${\ensuremath{\mu}}_{B}$, color ${\ensuremath{\mu}}_{8}$, and electric ${\ensuremath{\mu}}_{Q}$ chemical potentials is used. The contribution from free electrons to the free energy is added to take into account the $\ensuremath{\beta}$ 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 $\ensuremath{\beta}$ 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 $\ensuremath{\pi}$- and $\ensuremath{\sigma}$-meson masses are evaluated to be $\ensuremath{\sim}300\text{ }\text{ }\mathrm{MeV}$. 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 $\ensuremath{\sim}1100\text{ }\text{ }\mathrm{MeV}$ in the non-neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass $\ensuremath{\sim}|{\ensuremath{\mu}}_{Q}|\ensuremath{\sim}200\text{ }\text{ }\mathrm{MeV}$ appears in the gapless 2SC environment. For a stronger attraction in the diquark channel ($H=G$), there is again a resonance (with the mass $\ensuremath{\sim}300\text{ }\text{ }\mathrm{MeV}$) 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 ${\ensuremath{\mu}}_{B}=0$, as a function of $H$ has been investigated.