View source for Quark–lepton complementarity

{{More citations needed|date=January 2009}}

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
|pmid=10012286
 |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{{when|date=September 2018}} [[neutrino]] experiments confirm that the [[Pontecorvo–Maki–Nakagawa–Sakata matrix]] {{mvar|U}}{{sub|PMNS}} contains large{{clarify|date=August 2016}} [[Cabbibo angle|mixing angles]]. For example, atmospheric measurements of particle decay yield {{PhysicsParticle|''&theta;''|TR=PMNS|BR=23}}&nbsp;≈&nbsp;45°, while solar experiments yield {{PhysicsParticle|''&theta;''|TR=PMNS|BR=12}}&nbsp;≈&nbsp;34°. Compare these results with {{PhysicsParticle|''&theta;''|TR=PMNS|BR=13}}&nbsp;≈&nbsp;9° which is clearly smaller, at about {{sfrac|4}}~{{sfrac|3}}× the size,<ref>
{{cite journal
 |first1=F.P.  |last1=An           |first2=J.Z.  |last2=Bai
 |first3=A.B.  |last3=Balantekin   |first4=H.R.  |last4=Band
 |first5=D.    |last5=Beavis       |first6=W.    |last6=Beriguete
 |first7=M.    |last7=Bishai       |first8=S.    |last8=Blyth
 |first9=K.    |last9=Boddy        |first10=R.L. |last10=Brown
 |first11=B.   |last11=Cai         |first12=G.F. |last12=Cao
 |first13=J.   |last13=Cao         |first14=R.   |last14=Carr
 |first15=W.T. |last15=Chan        |first16=J.F. |last16=Chang
 |first17=Y.   |last17=Chang       |first18=C.   |last18=Chasman
 |first19=H.S. |last19=Chen        |first20=H.Y. |last20=Chen
 |first21=S.J. |last21=Chen        |first22=S.M. |last22=Chen
 |first23=X.C. |last23=Chen        |first24=X.H. |last24=Chen
 |first25=X.S. |last25=Chen        |first26=Y.   |last26=Chen
 |first27=Y.X. |last27=Chen        |first28=J.J. |last28=Cherwinka
 |first29=M.C. |last29=Chu         |first30=J.P. |last30=Cummings
 |display-authors=6
 |year=2012
 |title=Observation of electron–antineutrino disappearance at Daya Bay
 |journal=Physical Review Letters
 |volume=108  |issue=17  |page=171803
 |pmid=22680853  |bibcode=2012PhRvL.108q1803A  |s2cid=16580300
 |arxiv=1203.1669  |doi=10.1103/PhysRevLett.108.171803
}}
</ref>
and with the quark mixing angles in the [[Cabibbo–Kobayashi–Maskawa matrix]] {{mvar|U}}{{sub|CKM}}&nbsp;. 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}^\text{PMNS}+\theta_{12}^\text{CKM} \approx 45^\circ \,,</math>
:<math> \theta_{23}^\text{PMNS}+\theta_{23}^\text{CKM} \approx 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 {{mvar|V}}{{sub|M}} is roughly{{efn|
Since the [[Cabibbo–Kobayashi–Maskawa matrix|CKM]] relates quarks to quarks, and the [[Pontecorvo–Maki–Nakagawa–Sakata matrix|PMNS]] matrix relates leptons to leptons, the raw product uses “incompatible” co‑ordinates; at the very least, a [[unitary matrix]] should lie between them,{{citation needed|date=August 2021}} to rotate their axes into some kind of alignment of lepton co‑ordinates to quark co‑ordinates, before multiplying them. However, lacking a clear theoretical motivation for any particular rotation as-yet, the product with the matrix axes without any alignment serves to provide estimates which may need later adjustment.{{citation needed|date=August 2021}}
}}
defined as the product of the [[Cabibbo-Kobayashi-Maskawa matrix|CKM]] and [[Pontecorvo–Maki–Nakagawa–Sakata matrix|PMNS]] matrices:
:<math> V_\text{M} = U_\text{CKM} \cdot U_\text{PMNS} \, ,</math>

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

== Open questions ==
One may ask where the large lepton mixings come from, and whether this information is implicit in the form of the {{mvar|&thinsp;V}}{{sub|M&thinsp;}} 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 [[Pontecorvo–Maki–Nakagawa–Sakata matrix|PMNS]] mixing matrix can be obtained. In this class of models, the {{mvar|V}}{{sub|M}} matrix is determined by the heavy [[Majorana mass|Majorana]] neutrino mass matrix.

Despite the naïve relations between the [[Pontecorvo–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 {{mvar|&thinsp;V}}{{sub|M&thinsp;}} in models with renormalization effects that are relevant, however, only in particular cases with <math>\ \tan \beta > 40\ </math> and with quasi-degenerate neutrino masses.

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

== Footnotes ==
{{notelist}}

== References ==
{{reflist|25em}}

* {{cite journal |first1=B.C. |last1=Chauhan |first2=M. |last2=Picariello |first3=J. |last3=Pulido |first4=E. |last4=Torrente-Lujan |s2cid=118107624 |year=2007 |title=Quark–lepton complementarity, neutrino and standard model data predict {{math|''&theta;''}}{{su|p=PMNS|b=13}} {{math|{{=}}}} ({{val|9|+1|-2}})° |journal=[[European Physical Journal C]] |volume=50 |issue=3 |pages=573–578 |doi=10.1140/epjc/s10052-007-0212-z |arxiv=hep-ph/0605032 |bibcode=2007EPJC...50..573C }}
* {{cite journal |first=K.M. |last=Patel |s2cid=118623115 |year=2011 |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 |issue=1–4 |pages=225–230 |arxiv=1008.5061 |bibcode = 2011PhLB..695..225P}}

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