Quark-Lepton complementarity

Recent neutrino experiments confirm that the Pontecorvo-Maki-Nakagawa-Sakata(PMNS) lepton mixing matrix $U\_\{PMNS\}$ contains large mixing angles.For example the atmospheric mixing $heta\_\{23\}^\{PMNS\}$is compatible with $45^circ$,and the solar mixing $heta\_\{12\}^\{PMNS\}$ is$approx\; 34^circ$.These results should be compared with the third lepton mixing angle$heta\_\{13\}^\{PMNS\}$ which is very small and even compatible with zero,and with the quark mixing angles in the Cabibbo-Kobayashi-Maskawa matrix $U\_\{CKM\}$.

The disparity that nature indicates between quark and lepton mixingangles has been viewed in terms of a quark-lepton complementarity (QLC)which can be expressed in the relations:$heta\_\{12\}^\{PMNS\}+\; heta\_\{12\}^\{CKM\}simeq\; 45^circ,;quadquad\; heta\_\{23\}^\{PMNS\}+\; heta\_\{23\}^\{CKM\}simeq\; 45^circ,.$

Possible consequencesof QLC have been investigated in the literatureand in particular a simple correspondence between the$U\_\{PMNS\}$ and $U\_\{CKM\}$matrices has been proposedand analyzed in terms of a correlation matrix.The correlation matrix $V\_M$is simply defined as the product of the CKM and
PMNS matrices,$V\_M=U\_\{CKM\}cdot\; U\_\{PMNS\}$, and effortshave been made to obtain the most favorite patternfor the matrix $V\_M$. Unitarity then implies $U\_\{PMNS\}=U^\{dagger\}\_\{CKM\}V\_M$and one may ask where do the large lepton mixings come from?Is this information 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 determinedby the heavy Majorana neutrino mass matrix.

Despite the naive relations between the PMNSand CKM angles,a detailed analysis shows that the correlationmatrix is phenomenologically compatible with a
tribimaximal pattern, and only marginally witha bimaximal pattern.

It is possible to include bimaximalforms of the correlation matrix $V\_M$ in models with renormalization effects that are relevant, however,only in particular cases with large and with quasi degenerate neutrino masses.

References

* Bhag C. Chauhan, Marco Picariello, Joao Pulido, Emilio Torrente-Lujan," [http://arxiv.org/abs/hep-ph/0605032 Quark-lepton complementarity, neutrino and standard model data predict $heta\_\{13\}^\{PMNS\}=(9^\{+1\}\_\{-2\})^circ$] "," [http://www.springerlink.com/content/2k05123k40662738/ DOI: 10.1140/epjc/s10052-007-0212-z] ".