The quark–lepton complementarity (QLC) is a possible fundamental symmetry between

quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...

s and

lepton In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...

s. 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 The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...

at low energies, and hence quark–lepton symmetry may be realized in nature.

Possible evidence for QLC

Recent

neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...

experiments confirm that the Pontecorvo–Maki–Nakagawa–Sakata matrix contains large mixing angles. For example, atmospheric measurements of

particle decay In particle physics, particle decay is the spontaneous process of one unstable subatomic particle transforming into multiple other particles. The particles created in this process (the ''final state'') must each be less massive than the original ...

yield ≈ 45°, while solar experiments yield ≈ 34°. Compare these results with ≈ 9° which is clearly smaller, at about ~× the size, and with the quark mixing angles in the

Cabibbo–Kobayashi–Maskawa matrix In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength of the flavour-changing weak interaction. Technical ...

. 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_^\text+\theta_^\text \approx 45^\circ \,,

\theta_^\text+\theta_^\text \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 In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...

. The correlation matrix is roughly defined as the product of the CKM and PMNS matrices: :

V_\text = U_\text \cdot U_\text \, ,

Unitarity implies: :

U_\text = U^_\text V_\text \, .

Open questions

One may ask where the large lepton mixings come from, and whether this information is implicit in the form of the matrix. This question has been widely investigated in the literature, but its answer is still open. Furthermore, in some

Grand Unification Theories A Grand Unified Theory (GUT) is any Mathematical model, model in particle physics that merges the electromagnetism, electromagnetic, weak interaction, weak, and strong interaction, strong fundamental interaction, forces (the three gauge theory, ...

(GUTs) the direct QLC correlation between the CKM and the PMNS mixing matrix can be obtained. In this class of models, the 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 in models with

renormalization Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of the ...

effects that are relevant, however, only in particular cases with

\ \tan \beta > 40\

and with quasi-degenerate neutrino masses.

Footnotes

References

* * {{DEFAULTSORT:Quark-Lepton Complementarity Leptons Quarks Standard Model

Possible evidence for QLC

Open questions

See also

Footnotes

References