Nontrivial correlation between the CKM and MNS matrices

We point out that the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix VCKM and the Maki-Nakagawa-Sakata (MNS) lepton mixing matrix VMNS can naturally be correlated in a class of seesaw models if the Dirac neutrino mass matrix and the up-type quark mass matrix are symmetric and identical, but the texture of their correlation matrix Fν is rather nontrivial. The bimaximal mixing pattern of Fν is disfavored by current data, and other special forms of Fν may suffer from fine-tuning of the free phase parameters in fitting the so-called quark-lepton complementarity relation. A straightforward calculation of Fν in terms of VCKM and VMNS reveals a striking feature of Fν: its (1,3) element cannot be zero or too small, no matter whether the (1,3) elements of VCKM and VMNS are vanishing or not. We also add some brief comments on possible radiative corrections to VCKM and VMNS.