Primordial black holes and lepton flavor violation with scotogenic dark matter

We show that if the lepton flavor violating $\mu \rightarrow e \gamma$ process is observed in the MEG II experiment, the initial density of primordial black holes (PBHs) can be constrained with the scotogenic dark matter. As a benchmark case, if the PBH evaporation occurs in the radiation dominated era, the initial density may be $2\times 10^{-17} \lesssim \beta \lesssim 3 \times 10^{-16}$ for $\mathcal{O}$ (TeV) scale dark sector in the scotogenic model where $\beta=\rho_{\rm PBH}/\rho_{\rm rad}$ is the ratio of the PBH density $\rho_{\rm PBH}$ to the radiation density $\rho_{\rm rad}$ at the time of PBH formation. As an other benchmark case, if PBHs evaporate in the PBH dominated era, the initial density may be $1 \times 10^{-8} \lesssim \beta \lesssim 3 \times 10^{-7}$ for $\mathcal{O}$ (GeV) scale dark matter with other $\mathcal{O}$ (TeV) scale particles in the scotogenic model.