A modular A4 symmetric model of dark matter and neutrino

We propose a model based on modular A4 symmetry containing a dark matter candidate, realizing radiatively induced neutrino mass at one-loop level. One finds that stability of dark matter candidate can be assured by nonzero value of modular weight and heavy neutral fermion mass hierarchies, which include dark matter under the A4 triplet, are uniquely determined; MX≪M2<M3. Therefore we clearly identify single dark matter field which can discriminate from the other models with A4 modular symmetry. Then we discuss several phenomenological aspects and show predictions on the lepton sector. Especially, we find 0.56≲sin2⁡θ23≲0.624, which could have an advantage of this narrow region and be also discriminated from the other modular A4 models.