Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model

Abstract

We construct an extended version of the linear sigma model in such a way as to describe spin-$1$ hadrons as well as spin-$0$ hadrons in two-color QCD (QC${}_2$D) by respecting the Pauli-Gürsey $SU(4)$ symmetry. Within a mean-field approximation, we therefrom examine a mass spectrum of the spin-$1$ hadrons at finite quark chemical potential (${\mu }_q$) and zero temperature. Not only mean fields of scalar mesons and scalar-diquark baryons but also of vector mesons and vector-diquark baryons are incorporated. As a result, we find that, unless all of those four types of mean fields are taken into account, neither lattice result for the critical ${\mu }_q$ that corresponds to the onset of baryon superfluidity nor for ${\mu }_q$ dependence of the pion mass can be reproduced. We also find that a slight suppression of the $\rho$ meson mass in the superfluid phase, which was suggested by the lattice simulation, is reproduced by subtle mixing effects between spin-$0$ and spin-$1$ hadrons. Moreover, we demonstrate the emergence of an axialvector condensed phase and possibly of a vector condensed phase by identifying the values of ${\mu }_q$ at which the corresponding hadron masses vanish. The possible presence of iso-triplet $1^{-}$ diquarks that may be denoted by a tensor-type quark bilinear field is also discussed.

Comments: 24 pages, 11 figures