Quark–lepton complementarity

The quark–lepton complementarity (QLC) is a possible fundamental symmetry between quarks and leptons. First proposed in 1990 by Foot and Lew, 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.

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 θPMNS
23 ≈ 45°, while solar experiments yield θPMNS
12 ≈ 34°. These results should be compared with θPMNS
13 which is small, 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

$\theta_{12}^{PMNS}+\theta_{12}^{CKM}\simeq 45^\circ \ ,$

$\quad \quad \theta_{23}^{PMNS}+\theta_{23}^{CKM}\simeq 45^\circ \ .$

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 simply defined as the product of the CKM and PMNS matrices:

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

Unitarity implies:

$U_\mathrm{PMNS}=U^{\dagger}_\mathrm{CKM}V_\mathrm{M} \ .$

Open questions

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 determined by the heavy Majorana neutrino mass matrix.

Despite the naive 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 tanβ > 40 and with quasi-degenerate neutrino masses.

See also

• Leptoquark