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We propose a radiative seesaw model with a light dark matter candidate (DM)under modular $A_4$ and gauged $U(1)_{B-L}$ symmetries, in which neutrinomasses are generated via one-loop level, and we have a bosonic DM candidate$\sim 0.01-50$ GeV. DM is stabilized by nonzero modular weight and a remnant$Z_2$ symmetry of $U(1)_{B-L}$ symmetry. The naturalness of tiny DM mass isindirectly realized by the radiatively induced mass of neutral fermions thatinteract with our DM candidate. Thus, DM mass does not have to exceed theneutral fermion masses, whose scale is assumed to be 50 GeV. Taking severalbenchmark points of DM mass in DM analysis, we show the numerical analysis forthe neutrino oscillation data in the normal and inverted hierarchy cases andfind several features for both cases.

Modular $A_4$ symmetry and light dark matter with gauged $U(1)_{B-L}$