The examination of the EM interactions (equation ()) and weak interactions (equation ()) suggests that G essentially replaces . Therefore G has the dimension of while is dimensionless. By analogy to EM interactions which are mediated by photons, weak interactions are assumed to be mediated by vector bosons. In contrast to the photon, these vector bosons must be massive otherwise they would be directly produced in weak decays. Needless to say, the existence of these vector bosons and their masses have been confirmed experimentally. The decay amplitude is of the form:
where and q are the mass and the momentum carried by the vector boson mediating the interaction; g is the dimensionless weak coupling constant and the factor is inserted for the conventional definition of g. In the situations where (-decay and -decay for instance) the interaction is essentially at a point. By comparing equation () to () one has:
For illustration, consider the neutron- decay:
The decay amplitude is:
where and are the hadronic and the leptonic weak current:
The hadronic current can be rewritten as:
where and are the weak hadronic vector and axial-vector currents respectively. Following the arguments used in the EM case, becomes:
The similarity between and the EM current (equation ()) should be apparent. In EM, the charge is strictly conserved even for strong interacting particles. Furthermore, EM interactions are vector type of interactions with the coupling constant directly related to the charge:
The weak vector current is assumed to be conserved with a universal coupling constant in an analogy to the EM vector current. This assumption is the CVC hypothesis. The form factor in equation () vanishes as a result.
The CVC hypothesis can also be formulated using isospin formalism as follows: one defines a spinor
Using the Pauli matrices
the EM current and the weak vector current are written as:
The EM current consists of the isoscalar part which satisfies the current conservation requirement:
The isovector currents are as follows:
The CVC hypothesis assumes that these isovector currents are only different components of the same isospin current
is not conserved by itself unless a pionic contribution is added to it; in the case of neutron decay for instance, only a fraction of its lifetime neutron exists as a bare neutron; for the rest of its lifetime, the neutron is a proton surrounded by a "pion cloud". Like , needs to be supplemented with a pionic term to satisfy current conservation.
In conclusion, the assumption that the isovector currents
different components of the same current amounts to attributing the
same interaction strength to the pion-lepton vertices as to the baryon-lepton
vertices. Furthermore, since strong interactions are charge independent (to a
good approximation), one is led to the conservation of isospin --- pionic plus
baryonic --- which is a generalization of conservation of charge.