150 The very early universe
for instance, the formation of quark nuggets, the generation of magnetic fields
and gravitational waves, black hole formation, etc. These are still the subjects of
investigation. At present, however, it is unlikely that a quantum chromodynamics
phase transition leaves the observationally important “imprint.” It looks like an
interesting but rather “silent” epoch in the evolution of the universe.
4.3 Electroweak theory
The most familiar weak interaction process is neutron decay:n→peν ̄e.In Section
3.5 we described it using the Fermi four-fermion interaction theory, which is very
successful at low energies. However, this theory is not self-consistent because it
is not renormalizable and violates unitarity (conservation of probability) at high
energies (above 300 GeV). The Fermi constantGF,characterizing the strength
of the weak interactions, has dimension of inverse mass squared. Therefore, it is
natural to assume that the four-fermion vertex is simply the low-energy limit of
a diagram made of three-legged vertices with dimensionless couplinggw, which
describes the exchange of a massive vector bosonW(Figure 4.6).
At energies much smaller than the mass of the intermediate boson,one can
replace the boson propagator with 1/MW^2 and the diagram shrinks to the four-legged
diagram with effective coupling constantGF=O( 1 )g^2 w/MW^2 .Noting the vectorial
nature of the weak interactions, we are led to a description using gauge symmetries.
However, an obstacle immediately arises. We have noted above that gauge bosons
should be massless because the mass term spoils gauge invariance, renormalizability
and unitarity. This problem was finally resolved by the renormalizable standard
electroweak theory, where the masses of all particles (including intermediate gauge
bosons) emerge as a result of their interaction with a classical scalar field. The
electroweak theory is based on a unification (or, more precisely, on a “mixing”)
of electromagnetic and weak interactions within a model based onSU( 2 )×U( 1 )
pe−npW−e−n νe
νe∼
∼Fig. 4.6.