  We study the two-color QCD matter within two fundamental quark flavors via
both chiral perturbation theory and Nambu--Jona-Lasinio model methods. The
effective Lagrangian described by low lying meson and baryon, i.e., diquark, is
derived, where the excitations locate in the extended $\mathrm{SU}(4)$ flavor
symmetry space. We determine the leading order terms on the dependence of the
baryon and axial isospin densities. Then, the two-color NJL model is employed
to run the numerical simulation and the phase diagram in the plane of
$\mu-\nu_{5}$ is plotted.

High Energy Physics - Phenomenology;High Energy Physics - Theory;Nuclear Theory