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Effective interactions of axion supermultiplet and thermal production of axino dark matter

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_Φ< p < v_{PQ} is suppressed by (M_Φ^2)/(p^2) in addition to the well-known suppression by p/(16π^2 v_{PQ}), where M_Φis 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_Φis dominated by the production by matter supermultiplet, not by the production by gauge supermultiplet. Still the axino production rate is greatly reduced if M_Φ<< v_{PQ}, which would make the subsequent cosmology significantly altered. This would be most notable in the supersymmetric DFSZ model in which M_Φcorresponds 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.