  We discuss the effective interactions of axion supermultiplet, which might be
important for analyzing the cosmological aspect of supersymmetric axion model.
Related to axino cosmology, it is stressed that three seemingly similar but
basically different quantities, the Wilsonian axino-gluino-gluon coupling, the
1PI axino-gluino-gluon amplitude, and the PQ anomaly coefficient, should be
carefully distinguished from each other for correct analysis of the thermal
production of axinos in the early Universe. It is then noticed that the 1PI
axino-gluino-gluon amplitude at energy scale p in the range M_\Phi < p < v_{PQ}
is suppressed by (M_\Phi ^2)/(p^2) in addition to the well-known suppression by
p/(16\pi^2 v_{PQ}), where M_\Phi is the mass of the heaviest PQ-charged and
gauge-charged matter supermultiplet in the model, which can be well below the
PQ scale v_{PQ}. As a result, axino production at temperature T>M_\Phi is
dominated by the production by matter supermultiplet, not by the production by
gauge supermultiplet. Still the axino production rate is greatly reduced if
M_\Phi << v_{PQ}, which would make the subsequent cosmology significantly
altered. This would be most notable in the supersymmetric DFSZ model in which
M_\Phi corresponds to the Higgsino mass which is around the weak scale, however
a similar reduction is possible in the KSVZ model also. We evaluate the relic
axino density for both the DFSZ and KSVZ models while including the axino
production in the processes involving the heaviest PQ-charged and gauge-charged
matter supermultiplet.
