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The '''quark–lepton complementarity''' (QLC) is a possible fundamental symmetry between [[quark]]s and [[lepton]]s. First proposed in 1990 by Foot and Lew,<ref name="FootLew">
{{cite journal
 |author=R. Foot, H. Lew
 |title=Quark-lepton-symmetric model
 |journal=[[Physical Review D]]
 |volume=41 |issue=11 |pages=3502–3505
 |year=1990
 |doi=10.1103/PhysRevD.41.3502
|bibcode = 1990PhRvD..41.3502F }}</ref> it assumes that leptons as well as quarks come in three "[[Color charge|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''<sub>PMNS</sub> contains large [[mixing angle]]s{{disambiguation needed|date=August 2012}}. For example, atmospheric measurements of particle decay yield {{PhysicsParticle|''&theta;''|TR=PMNS|BR=12}}&nbsp;≈&nbsp;45°, while solar experiments yield {{PhysicsParticle|''&theta;''|TR=PMNS|BR=12}}&nbsp;≈&nbsp;34°. These results should be compared with {{PhysicsParticle|''&theta;''|TR=PMNS|BR=13}} which is small,<ref>F. P. An et al.  [DAYA-BAY Collaboration], Phys. Rev. Lett.  108, 171803 (2012) [arXiv:1203.1669 [hep-ex]] http://arxiv.org/abs/arXiv:1203.1669</ref> and with the quark mixing angles in the [[Cabibbo–Kobayashi–Maskawa matrix]] ''U''<sub>CKM</sub>. 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
:<math> \theta_{12}^{PMNS}+\theta_{12}^{CKM}\simeq 45^\circ \ ,</math>
:<math> \quad \quad \theta_{23}^{PMNS}+\theta_{23}^{CKM}\simeq 45^\circ \ .</math>

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''<sub>M</sub> is simply defined as the product of the [[Cabibbo-Kobayashi-Maskawa matrix|CKM]] and [[Maki-Nakagawa-Sakata Matrix|PMNS]] matrices:
:<math>V_\mathrm{M}=U_\mathrm{CKM} \cdot  U_\mathrm{PMNS} \ ,</math>

[[Unitarity]] implies:
:<math>U_\mathrm{PMNS}=U^{\dagger}_\mathrm{CKM}V_\mathrm{M} \ .</math>

== Open questions ==

One may ask where do the large lepton mixings come from? Is this information implicit in the form of the ''V''<sub>M</sub> 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 [[Cabibbo-Kobayashi-Maskawa matrix|CKM]] and the [[Maki-Nakagawa-Sakata Matrix|PMNS]] mixing matrix can be obtained. In this class of models, the <math>V_M</math> matrix is determined by the heavy [[Majorana mass|Majorana]] neutrino mass matrix.

Despite the naive relations between the [[Maki-Nakagawa-Sakata Matrix|PMNS]] and [[Cabibbo-Kobayashi-Maskawa matrix|CKM]] angles,
a detailed analysis shows that the correlation matrix is phenomenologically compatible with a [[Tribimaximal mixing|tribimaximal]] pattern, and only marginally with a [[bimaximal]] pattern. It is possible to include [[bimaximal]] forms of the correlation matrix ''V''<sub>M</sub> in models with renormalization effects that are relevant, however, only in particular cases with tan''β''&nbsp;>&nbsp;40 and with quasi-degenerate neutrino masses.

==See also==
*[[Leptoquark]]

==References==
<references />
*{{cite journal
 |author=B.C. Chauhan, M. Picariello, J. Pulido, E. Torrente-Lujan
 |title=Quark-lepton complementarity, neutrino and standard model data predict ''&theta;''{{su|p=PMNS|b=13}} {{=}} {{val|9|+1|-2}} &deg;
 |journal=[[European Physical Journal C]]
 |volume=50 |issue=3 |pages=573–578
 |doi=10.1140/epjc/s10052-007-0212-z
 |arxiv=hep-ph/0605032
 |year=2007
|bibcode = 2007EPJC...50..573C }}

*{{cite journal
 |author=K.M. Patel
 |title=An ''SO''(10) × ''S''<sub>4</sub> Model of Quark-Lepton Complementarity;
 |journal=[[Physics Letters B]] 
 |doi=10.1016/j.physletb.2010.11.024
 |volume=695
 |arxiv=1008.5061
 |page=225
 |year=2010
|bibcode = 2011PhLB..695..225P }}

{{DEFAULTSORT:Quark-Lepton Complementarity}}
[[Category:Leptons]]
[[Category:Quarks]]
[[Category:Standard Model]]
[[Category:Particle physics]]