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 nuclei. All commonly ...
s and
lepton
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
s. First proposed in 1990 by Foot and Lew,
[
] it assumes that leptons as well as quarks come in three "
colors
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associa ...
". Such theory may reproduce the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
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 a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
experiments confirm that the
Pontecorvo–Maki–Nakagawa–Sakata matrix
In particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary
mixing matrix which contains information on the mismat ...
contains large
mixing angles. For example, atmospheric measurements of particle decay 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 which contains information on the strength of the flavour-changing weak interaction. Technicall ...
. 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
:
:
Note that the magic angle of
is as the same theoretical derivation by theoretical physicist Hung-Te Su in Taiwan, whose two papers has been under review on Phys. Lett. B and is ready to be published on Phys. Rev. C, respectively.
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:
:
Unitarity
In quantum physics, unitarity is the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of qua ...
implies:
:
Open questions
One may ask where do the large lepton mixings come from? Is this information 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 a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this ...
(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 naive 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 effects that are relevant, however, only in particular cases with
and with quasi-degenerate neutrino masses.
See also
*
Leptoquark
Leptoquarks (LQs) are hypothetical particles that would interact with quarks and leptons. Leptoquarks are color-triplet bosons that carry both lepton and baryon numbers. Their other quantum numbers, like spin, (fractional) electric charge and weak ...
Footnotes
References
*
*
{{DEFAULTSORT:Quark-Lepton Complementarity
Leptons
Quarks
Standard Model