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R. N. Mohapatra
interactions, called the four-Fermi theory.
1 When Marshak and Sudarshan et
al. proposed the V − A theory, the evidence against it was overwhelming—
so it took them courage to defy the existing experimental results to propose
the theory. Experiments which were against the V − A theory when it was
proposed were found to be wrong. The V − A theory was confirmed soon
after it was proposed and continued to remain the theory of weak interactions
until it became part of the standard model.
The V − A theory suggested that there might be spin one bosons, which
behave like the light quantum, the photon, but had a large mass that could be
mediating the V − A interactions. Do these bosons arise from a fundamental
principle, also similar to what gives rise to the existence of photons—the
gauge invariance? As just noted, the Yang–Mills generalization of gauge
invariance looked just right for weak forces. However, it had the mediating
particles W , Z, very similar to the photon, and therefore had infinite range,
as noted.The weak forces, however, have a very short range, which means the
W , Z must have a mass. A profound theoretical part of the story, i.e. how to
assign mass to the W and Z, was still missing.
11.2 Where Did Mass Come from?
A very simple way to cure the mass problem of the W and Z is to simply add a
mass to the theory and declare that they are massive. Things are, however, not
as simple. There are requirements of consistency in a theory. One consistency
requirement in Quantum Field Theory is that the theory should be able to
produce numbers that can be used to test it. This requirement in physics
language is called renormalizability. The adhoc addition of a mass for the
W , Z to the Yang–Mills theory may be easy to imagine but hard to make
consistent with the requirement of renormalizability. Another way to state the
idea is, adding an adhoc mass makes the theory behave badly at high energies. A
theory that cannot be tested is not much of a theory and will be soon discarded
by the community. A new way of applying mass had to be sought. This is
called spontaneous symmetry breaking, discussed in the next section. We start
this discussion with an illustration of what symmetry and symmetry breaking
mean.
1 The same year after Marshak and Sudarshan’s theory was announced at a meeting in Venice, Sudarshan
and Marshak discussed this theory with Murray Gell-Mann at a RAND corporation meeting. A
few months later, Richard Feynman and Murray Gell-Mann derived the same theory using different
arguments.
R. N. Mohapatra
interactions, called the four-Fermi theory.
1 When Marshak and Sudarshan et
al. proposed the V − A theory, the evidence against it was overwhelming—
so it took them courage to defy the existing experimental results to propose
the theory. Experiments which were against the V − A theory when it was
proposed were found to be wrong. The V − A theory was confirmed soon
after it was proposed and continued to remain the theory of weak interactions
until it became part of the standard model.
The V − A theory suggested that there might be spin one bosons, which
behave like the light quantum, the photon, but had a large mass that could be
mediating the V − A interactions. Do these bosons arise from a fundamental
principle, also similar to what gives rise to the existence of photons—the
gauge invariance? As just noted, the Yang–Mills generalization of gauge
invariance looked just right for weak forces. However, it had the mediating
particles W , Z, very similar to the photon, and therefore had infinite range,
as noted.The weak forces, however, have a very short range, which means the
W , Z must have a mass. A profound theoretical part of the story, i.e. how to
assign mass to the W and Z, was still missing.
11.2 Where Did Mass Come from?
A very simple way to cure the mass problem of the W and Z is to simply add a
mass to the theory and declare that they are massive. Things are, however, not
as simple. There are requirements of consistency in a theory. One consistency
requirement in Quantum Field Theory is that the theory should be able to
produce numbers that can be used to test it. This requirement in physics
language is called renormalizability. The adhoc addition of a mass for the
W , Z to the Yang–Mills theory may be easy to imagine but hard to make
consistent with the requirement of renormalizability. Another way to state the
idea is, adding an adhoc mass makes the theory behave badly at high energies. A
theory that cannot be tested is not much of a theory and will be soon discarded
by the community. A new way of applying mass had to be sought. This is
called spontaneous symmetry breaking, discussed in the next section. We start
this discussion with an illustration of what symmetry and symmetry breaking
mean.
1 The same year after Marshak and Sudarshan’s theory was announced at a meeting in Venice, Sudarshan
and Marshak discussed this theory with Murray Gell-Mann at a RAND corporation meeting. A
few months later, Richard Feynman and Murray Gell-Mann derived the same theory using different
arguments.