Nontrivial Correlation between the CKM and MNS Matrices

Abstract

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

RevTex 12 pages (1 PS figure)

References in corpus (3)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Possible Gauge Theoretic Origin for Quark-Lepton Complementarity
• Fermion Masses and Flavor Mixing in A Supersymmetric SO(10) Model

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