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,^[1] 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^[when?] neutrino experiments confirm that the Pontecorvo–Maki–Nakagawa–Sakata matrix $U$ _PMNS contains large^{[clarification needed]} mixing angles. For example, atmospheric measurements of particle decay yield
θ^PMNS
₂₃ ≈ 45°, while solar experiments yield
θ^PMNS
₁₂ ≈ 34°. Compare these results with
θ^PMNS
₁₃ ≈ 9° which is clearly smaller, at about ⁠1/4⁠~⁠1/3⁠× the size,^[2] 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}^{\text{PMNS}}+\theta _{12}^{\text{CKM}}\approx 45^{\circ }\,,

\theta _{23}^{\text{PMNS}}+\theta _{23}^{\text{CKM}}\approx 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 roughly^[a] defined as the product of the CKM and PMNS matrices:

V_{\text{M}}=U_{\text{CKM}}\cdot U_{\text{PMNS}}\,,

Unitarity implies:

U_{\text{PMNS}}=U_{\text{CKM}}^{\dagger }V_{\text{M}}\,.

Open questions

One may ask where the large lepton mixings come from, and whether this information is 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 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 $V$ _M in models with renormalization effects that are relevant, however, only in particular cases with $\ \tan \beta >40\$ and with quasi-degenerate neutrino masses.

Footnotes

^ 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]} 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]}

References

^ R. Foot, H. Lew (1990). "Quark-lepton-symmetric model". Physical Review D. 41 (11): 3502–3505. Bibcode:1990PhRvD..41.3502F. doi:10.1103/PhysRevD.41.3502. PMID 10012286.
^ An, F.P.; Bai, J.Z.; Balantekin, A.B.; Band, H.R.; Beavis, D.; Beriguete, W.; et al. (2012). "Observation of electron–antineutrino disappearance at Daya Bay". Physical Review Letters. 108 (17): 171803. arXiv:1203.1669. Bibcode:2012PhRvL.108q1803A. doi:10.1103/PhysRevLett.108.171803. PMID 22680853. S2CID 16580300.

Chauhan, B.C.; Picariello, M.; Pulido, J.; Torrente-Lujan, E. (2007). "Quark–lepton complementarity, neutrino and standard model data predict $θ$ ^PMNS
₁₃ $=$ (9+1
−2)°". European Physical Journal C. 50 (3): 573–578. arXiv:hep-ph/0605032. Bibcode:2007EPJC...50..573C. doi:10.1140/epjc/s10052-007-0212-z. S2CID 118107624.
Patel, K.M. (2011). "An SO(10) × S₄ Model of Quark–Lepton Complementarity". Physics Letters B. 695 (1–4): 225–230. arXiv:1008.5061. Bibcode:2011PhLB..695..225P. doi:10.1016/j.physletb.2010.11.024. S2CID 118623115.

[3] 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]} 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]}

[FootLew-1] R. Foot, H. Lew (1990). "Quark-lepton-symmetric model". Physical Review D. 41 (11): 3502–3505. Bibcode:1990PhRvD..41.3502F. doi:10.1103/PhysRevD.41.3502. PMID 10012286.

[2] An, F.P.; Bai, J.Z.; Balantekin, A.B.; Band, H.R.; Beavis, D.; Beriguete, W.; et al. (2012). "Observation of electron–antineutrino disappearance at Daya Bay". Physical Review Letters. 108 (17): 171803. arXiv:1203.1669. Bibcode:2012PhRvL.108q1803A. doi:10.1103/PhysRevLett.108.171803. PMID 22680853. S2CID 16580300.

[1]

[2]

[a]

Possible evidence for QLC

Open questions

See also

Footnotes

References