  We investigate modifications of hadron masses at finite quark chemical
potential in two-flavor and two-color QCD, of which the data are available from
lattice simulations, within a linear sigma model based on approximate
Pauli-Gursey $SU(4)$ symmetry. The model describes not only ground-state scalar
diquarks and pseudo-scalar mesons but also the excited pseudo-scalar diquarks
and scalar mesons; each ground-state diquark (meson) has the corresponding
excited diquark (hadron) with opposite parity as a chiral partner. Effects of
chiral symmetry breaking and diquark condensates are incorporated by a
mean-field treatment. We show that various mixings among the hadrons, which are
triggered by the breakdown of baryon number conservation in the superfluid
phase, lead to a rich hadron mass spectrum. We discuss the influence of
$U(1)_A$ anomaly on the density dependence of the mass spectrum and also
manifestations of the chiral partner structures as density increases in the
superfluid phase. The predicted hadron masses are expected to provide future
lattice simulations with useful information on such symmetry properties in
dense two-color QCD.
