Probing lepton flavor violation with nonzero $U_{e3}$ and leptogenesis through $A_4$ symmetry breaking

We study how lepton flavor violation (LFV) is related to the reactor angle $\theta_{13}$, LHC/dark matter (DM) signal with a successful leptogenesis in a radiative seesaw model through $A_4$ flavor symmetry breaking, in the light of the deviation of tri-bimaximal mixing (TBM) angles and the recent precision oscillation data. To do this, we consider the normal mass spectrum of light neutrino giving a successful leptogenesis at electroweak (EW) scale or more with a relatively large $\sin\theta_{13}\simeq{\cal O}(0.1)$, where a successful leptogenesis requires LHC/DM signal $m_{-}\lesssim$ a few keV in our scenario, and we show that the measurement of $\tau\rightarrow\mu\gamma$ is strongly dependent on $m_{-}$ and the leptogenesis scale. Especially, we show that $\mu\rightarrow e\gamma$ and $\mu-e$ conversion are proportional to the value of $\theta_{13}$, and the measurements of both $\mu\rightarrow e\gamma$ (and/or $\mu-e$ conversion) and $\theta_{13}$ can give a prediction of $\tau\rightarrow\mu\gamma$ with a successful leptogenesis.