TeV-scale seesaw with non-negligible left-right neutrino mixings

We suggest natural TeV-scale seesaw with non-negligible left-right neutrino mixings as preserving tiny neutrino masses. Our analysis is exhibited, without loss of generality, by taking a basis of the neutrino matrices, in which the condition to obtain the left-right mixings is clear. We also suggest a flavor symmetry as an underlying theory, which naturally realizes our setup to preserve tiny neutrino masses. Our setup can predict a magnitude of sin theta_13 in a region of 0.10 to 0.20, depending on the deviation from maximal atmospheric neutrino mixing and CP phase. We also investigate experimental constraints and phenomenology in our setup.