Quark–lepton complementarity

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}} mixing angles. For example, atmospheric measurements of particle decay yield {{PhysicsParticle|θ|TR=PMNS|BR=23}} ≈ 45°, while solar experiments yield {{PhysicsParticle|θ|TR=PMNS|BR=12}} ≈ 34°. Compare these results with {{PhysicsParticle|θ|TR=PMNS|BR=13}} ≈ 9° which is clearly smaller, at about {{sfrac|4}}~{{sfrac|3}}× the size,

{{cite journal

|first1=F.P. |last1=An |first2=J.Z. |last2=Bai

|first3=A.B. |last3=Balantekin |first4=H.R. |last4=Band

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|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

}}

and with the quark mixing angles in the Cabibbo–Kobayashi–Maskawa matrix {{mvar|U}}{{sub|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

:$\backslash theta\_\{12\}^\backslash text\{PMNS\}+\backslash theta\_\{12\}^\backslash text\{CKM\}\; \backslash approx\; 45^\backslash circ\; \backslash ,,$

:$\backslash theta\_\{23\}^\backslash text\{PMNS\}+\backslash theta\_\{23\}^\backslash text\{CKM\}\; \backslash approx\; 45^\backslash circ\; \backslash ,.$

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 CKM relates quarks to quarks, and the 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 CKM and PMNS matrices:

:$V\_\backslash text\{M\}\; =\; U\_\backslash text\{CKM\}\; \backslash cdot\; U\_\backslash text\{PMNS\}\; \backslash ,\; ,$

Unitarity implies:

:$U\_\backslash text\{PMNS\}\; =\; U^\{\backslash dagger\}\_\backslash text\{CKM\}\; V\_\backslash text\{M\}\; \backslash ,\; .$

One may ask where the large lepton mixings come from, and whether this information is implicit in the form of the {{mvar| V}}{{sub|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 {{mvar|V}}{{sub|M}} 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 {{mvar| V}}{{sub|M }} in models with renormalization effects that are relevant, however, only in particular cases with $\backslash \; \backslash tan\; \backslash beta\; >\; 40\backslash$ and with quasi-degenerate neutrino masses.

• Leptoquark

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{{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|θ}}{{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) × S₄ 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