  We investigate effects of the axial anomaly term with a chiral-diquark
coupling on the phase diagram within a two-plus-one-flavor Nambu-Jona-Lasinio
(NJL) model under the charge-neutrality and $\beta$-equilibrium constraints. We
find that when such constraints are imposed, the new anomaly term plays a quite
similar role as the vector interaction does on the phase diagram, which the
present authors clarified in a previous work. Thus, there appear several types
of phase structures with multiple critical points at low temperature $T$,
although the phase diagrams with intermediate-$T$ critical point(s) are never
realized without these constraints even within the same model Lagrangian. This
drastic change is attributed to an enhanced interplay between the chiral and
diquark condensates due to the anomaly term at finite temperature; the u-d
diquark coupling is strengthened by the relatively large chiral condensate of
the strange quark through the anomaly term, which in turn definitely leads to
the abnormal behavior of the diquark condensate at finite $T$, inherent to the
asymmetric quark matter. We note that the critical point from which the
crossover region extends to zero temperature appears only when the strength of
the vector interaction is larger than a critical value. We also show that the
chromomagnetic instability of the neutral asymmetric homogenous two-flavor
color superconducting(2CSC) phase is suppressed and can be even completely
cured by the enhanced diquark coupling due to the anomaly term and/or by the
vector interaction.
