2.1.3 Cabibbo Theory and Unitarity of the CKM-Matrix
While the weak interaction conserves the lepton number, it violates the
conservation of the quark flavour. This was observed in rare decays which
showed that strangeness, for instance, was not a good quantum number. Rather
than introducing quark-quark coupling constants, Cabibbo, in order to preserve
universality, proposed the new quark eigenstates
and
.
They are calculated by rotation of the quark eigenstates of the
flavour-preserving strong interaction. For example
=
ssin q C + dcos q C, with
q C being the Cabibbo mixing-angle. The generalization by
Glashow, Iliopoulos and Maiani in 1970 led to the proposal of the C-quark by
Bjørken and Glashow as a consequence of (weak) isospin symmetry. After
the discovery of CP-violation in 1964, Kobayashi and Maskawa extended the model
by introducing phase factors and proposing a third generation of heavier
quarks. The quark-mixing between the three generations is summarized in the CKM
mixing matrix.
.
Now vector coupling can be related directly to leptonic decays. Due to the
absence of quark-mixing in leptonic decay, because of universality, the vector
coupling constant can be expressed in terms of the muon decay constant
Gµ = GV/Vud The matrix element
Vud therefore can be determined by measuring the pion beta decay
branching ratio. The further elements of the first row - as recommended by
[PDG98] - are 0.2196±0.0023 for Vus and 0.00316±0.0009
Vub.
The classification of elementary particles and their interactions, furthermore
the successful discovery of proposed fundamental particles like the gauge
vector bosons of electroweak interaction [Ua183a,Ua183b] and the t-quark
[Aba95,Abe95], makes the standard model (SM) a trusted fundament of modern
physics. Controversially, the phenomenological ansatz with 18 free parameters
and the purpose to find a unified quantum field-theory description of the
fundamental interactions would make an extension of the standard model
desirable. Among the possibilities we mention the Minimal Supersymmetric
Standard Model and the String model. They are suggesting either an additional
set of elementary particles or more fundamental constituents of the particles
currently considered elementary. These elementary particles are classified into
three families of quarks and leptons each. Unexplained evidence like the
presence of a chiral symmetry group which is parity violating, the origins of
mass, mixing angles and CP-violating phase give raise for possible physics
beyond standard model.
The standard model predicts the unitarity of the CKM matrix. A distinct
deviation from this demands an expansion of the standard model or new physics.
The main concepts are briefly summarized:
* Existence of a fourth generation of heaviest quarks and - presumably -
leptons[6].
* A supersymmetric extension of the minimal SM predicts the existence of a
bosonic partner of every fundamental fermion and a fermionic partner of every
fundamental boson. The supersymmetric partners are considered to be heavier
than 100 GeV; but the exchange of supersymmetric particles would affect muon
and B-meson decays, for example. The effect of electroweak symmetry breaking
also would violate the conservation of lepton numbers. [Moh92]
* The existence of a right handed WR gauge boson would result in an
admixture of (V+A)-interactions to the (V-A)-theory [Wil94].
* Additional neutral gauge bosons Z' - which are predicted by some `Grand
Unification Theory' models - would lead to higher order corrections for the
calculation of the decay rate due to possible quantum loop
corrections.[Mar87]
* Compositeness of elementary fermions and vector gauge bosons would lead to a
correction of the quark mixing angles.[Sir89]
[6] This would demand a heavy neutrino with a mass
beyond half a W-Boson mass