Importance of Threshold Corrections in Quark-Lepton Complementarity

The recent experimental measurements of the solar neutrino mixing angle $\theta_{sol}$ and the Cabibbo mixing angle $\theta_C$ reveal a surprising relation, $\theta_{sol}+\theta_C \simeq \frac{\pi}{4}$. We note that the lepton mixing matrix derived from quark-lepton unification can lead to a shift of the complementarity relation at low energy. While the renormalization group effects generally lead to additive contribution on top of the shift, in this letter, we show that the threshold corrections which may exist in some intermediate scale new physics such as supersymmetric standard model can diminish it, so we can achieve the complementarity relation at a low energy. Finally, we discuss a possibility to achieve the complementarity relation at a high energy by taking particular form of non-symmetric form of down Yukawa matrix.