The quark–lepton complementarity (QLC) is a possible fundamental symmetry between quarks and leptons. First proposed in 1990 by Foot and Lew,[1] it assumes that leptons as well as quarks come in three "colors". Such theory may reproduce the Standard Model at low energies, and hence quark–lepton symmetry may be realized in nature.
Recent neutrino experiments confirm that the Pontecorvo–Maki–Nakagawa–Sakata matrix contains large mixing angles. For example, atmospheric measurements of particle decay yield ≈ 45°, while solar experiments yield ≈ 34°. Compare these results with ≈ 9° which is clearly smaller, at about ~× the size,[2] and with the quark mixing angles in the Cabibbo–Kobayashi–Maskawa matrix . 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
| CKM | |
| \theta | |
| 12 |
≈ 45\circ,
| CKM | |
| \theta | |
| 23 |
≈ 45\circ.
VM=UCKM ⋅ UPMNS,
Unitarity implies:
UPMNS=
| \dagger | |
| U | |
| CKM |
VM.
One may ask where the large lepton mixings come from, and whether this information is implicit in the form of the 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 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 in models with renormalization effects that are relevant, however, only in particular cases with
\tan\beta>40