Quark–lepton complementarity

Recent^[when?] neutrino experiments confirm that the Pontecorvo–Maki–Nakagawa–Sakata matrix U_PMNS contains large^{[clarification needed]} 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,^[2] 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^[a] defined as the product of the CKM and PMNS matrices:

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

Unitarity implies:

${\displaystyle U_{\text{PMNS}}=U_{\text{CKM}}^{\dagger }V_{\text{M}}\,.}$ 

One may ask where the large lepton mixings come from, and whether this information is implicit in the form of the  V_M matrix. This question has been widely investigated in the literature, but its answer is still open. Furthermore, in some Grand Unification Theories (GUTs) the direct QLC correlation between the CKM and the PMNS mixing matrix can be obtained. In this class of models, the V_M matrix is determined by the heavy Majorana neutrino mass matrix.

Despite the naïve relations between the PMNS and CKM angles, a detailed analysis shows that the correlation matrix is phenomenologically compatible with a tribimaximal pattern, and only marginally with a bimaximal pattern. It is possible to include bimaximal forms of the correlation matrix  V_M in models with renormalization effects that are relevant, however, only in particular cases with ${\displaystyle \ \tan \beta >40\ }$  and with quasi-degenerate neutrino masses.

• Leptoquark

• Chauhan, B.C.; Picariello, M.; Pulido, J.; Torrente-Lujan, E. (2007). "Quark–lepton complementarity, neutrino and standard model data predict θ^PMNS
  ₁₃ = (9+1
  −2)°". European Physical Journal C. 50 (3): 573–578. arXiv:hep-ph/0605032. Bibcode:2007EPJC...50..573C. doi:10.1140/epjc/s10052-007-0212-z. S2CID 118107624.
• Patel, K.M. (2011). "An SO(10) × S₄ Model of Quark–Lepton Complementarity". Physics Letters B. 695 (1–4): 225–230. arXiv:1008.5061. Bibcode:2011PhLB..695..225P. doi:10.1016/j.physletb.2010.11.024. S2CID 118623115.