Quark–lepton complementarity

Possible evidence for QLC

Recent neutrino experiments confirm that the Pontecorvo–Maki–Nakagawa–Sakata matrix U_PMNS contains large mixing angles. For example, atmospheric measurements of particle decay yield
θ^PMNS
₂₃ ≈ 45°, while solar experiments yield
θ^PMNS
₁₂ ≈ 34°. Compare these results with
θ^PMNS
₁₃ ≈ 9° which is clearly smaller, at about ⁠1/4⁠~⁠1/3⁠× the size, and with the quark mixing angles in the Cabibbo–Kobayashi–Maskawa matrix U_CKM . The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a "quark–lepton complementarity" which can be expressed in the relations

${\displaystyle {\theta }_{12}^{\text{PMNS}}+{\theta }_{12}^{\text{CKM}}\approx {45}^{\circ },}$

${\displaystyle {\theta }_{23}^{\text{PMNS}}+{\theta }_{23}^{\text{CKM}}\approx {45}^{\circ }.}$

Possible consequences of QLC have been investigated in the literature and in particular a simple correspondence between the PMNS and CKM matrices have been proposed and analyzed in terms of a correlation matrix. The correlation matrix V_M is roughly defined as the product of the CKM and PMNS matrices:

${\displaystyle V_{\text{M}}=U_{\text{CKM}}\cdot U_{\text{PMNS}},}$

Unitarity implies:

${\displaystyle U_{\text{PMNS}}=U_{\text{CKM}}^{†}{V}_{\text{M}}.}$