CHAPTER FIVE
Model, are sometimes said to predict mass-values. But, as a closer
inspection reveals, certain parameters, as, e.g., the “weak mixing angle”
(Weinberg angle), have to be inserted in order to reach agreement
with experience. Furthermore, the Standard Model, which employs
the principle of local gauge invariance and the notion of spontaneous
symmetry breaking, also incorporates a mechanism that endows par-
ticles with mass. Known as the Higgs mechanism, it was developed
by Peter Higgs in 1964 in order to introduce mass into the Yang-Mills
gauge theories.
48
Abdus Salam and independently Steven Weinberg
soon recognized its crucial importance for their attempts to unify the
theories of the weak nuclear force and the electromagnetic force into a
unified gauge theory of a single “electroweak” force. The difficulty they
hoped to resolve by means of the Higgs mechanism was the fact that the
carriers of the weak interaction, the W
+
, W
−
, and Z bosons have masses
as large as those of moderate-sized nuclei, whereas the corresponding
carriers of the electromagnetic force have no mass at all. Since the Higgs
mechanism did indeed remove the last stumbling block on the road
to a unified electroweak theory, it is often credited with explaining the
“origin” or “genesis” of mass.
49
But if a process “generates” mass it may
reasonably be expected to provide information about the nature of what
it “generates” as well.
In order to see whether this is really the case we should, of course,
know the “machinery” of this mechanism, that is the procedure by
which spontaneous symmetry-breaking endows gauge fields of zero
mass with mass. It would lead us too far into mathematical detail to
present a quantitative account of this procedure. Suffice it to point out
that the Higgs mechanism is based on the assumption of the existence
of a scalar field, the “Higgs field,” which permeates all of space. By
coupling with this field a massless particle acquires a certain amount
of potential energy and, hence, according to the mass-energy relation, a
certain mass. The stronger the coupling, the more massive the particle.
The critical phase of this process can be illustrated as follows:
50
48
P. W. Higgs, “Broken Symmetry, Massless Particles and Gauge Fields,” Physics Let-
ters 12, 132–133 (1964); “Spontaneous Symmetry Breakdown Without Massless Bosons,”
Physical Review 145, 1156–1163 (1966).
49
See, e.g., R. Castmore and C. Sutton, “The Origin of Mass,” New Scientist 145, 35–39
(1992). Y. Nambu, “A Matter of Symmetry: Elementary Particles and the Origin of Mass,”
The Sciences 32 (May/June), 37–43 (1992). J. LaChapelle, “Generating Mass Without the
Higgs Particle,” Journal of Mathematical Physics 35, 2199–2209 (1994).
50
M.J.G. Veltman, “The Higgs Boson,” Scientific American 255 (November), 88–94 (1986).
162