CHIRAL SYMMETRY BREAKING!
We have discussed the possible
role of electroweak symmetry breaking in the origin of at least
part of the matter-antimatter asymmetry in our universe.
But it has been realized for decades that the breaking of chiral
symmetry, once the universe fell below the electroweak
unification temperature, had a major role to play in the origin
of almost all the mass of ordinary matter! Remember that
the weak interaction violates parity conservation to the largest
extent possible. It also breaks chiral symmetry, again to the
maximal amount. ONLY quarks and leptons with left-hand chirality
participate in the weak interaction. [Antiquarks and antileptons
with right-handed chirality also participate, of course.] And
neutrinos of right-hand chirality don't even exist, as far as we
know! We discussed this topic very briefly earlier, as part of a
presentation of basic features of the electroweak theory. Now we
need to take a slightly closer look. Remember that in both
the electroweak theory and in QCD, before interaction with the
Higgs field is allowed, all mass terms are ZERO. Therefore
QCD also has chiral symmetry, before a Higgs-field interaction
breaks it.
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Remember that the masses of the u
and d quarks are only a few MeV, yet the “constituent” quark
mass is 940/3 or around 310 MeV. Also, we emphasize again that
the standard model theories of strong, weak and electromagnetic
interactions start with massless quarks and leptons.
Their mass is generated later by coupling to the Higgs field.
But the fact that the basic equations of the Standard Model
involve massless particles creates yet another symmetry, chiral
symmetry. Chirality is a Lorentz-invariant generalization
of the concept of helicity, or handedness, which we have also
previously discussed briefly. Massless particles are
eigenstates of helicity, and have a definite chirality. When the
Higgs coupling is turned on, the chiral symmetry is also broken.
In the same way that the Higgs mechanism generates mass, the
chiral symmetry breaking also generates additional mass. The
proton and neutron are full of virtual quark-antiquark pairs,
but before chiral symmetry breaking the vacuum expectation value
of the mass of a virtual quark-antiquark pair is zero.
After symmetry-breaking, it is not zero. Mass generation by the
chiral symmetry breaking is most significant only for the
lightest quarks, the u, d and s. But notice that the mass
generated for the u and d quarks is the principal source of
almost all the mass of ordinary matter, 98% of it to be more
precise! In other words, the virtual quark-antiquark pairs
within the nucleon now make a major contribution to its total
mass.
Chiral symmetry and its
breaking are as fundamental a feature of QCD as quark or color
confinement, and asymptotic freedom!
The telltale signs of the symmetry
breaking in our universe today, apart from nucleon mass,
are a distinctive splitting by 500 MeV of the
orginally-degenerate “chiral partner” states of mesons and
baryons, and the appearance of pseudo-Goldstone bosons (the
pions).
Here,
written at the level of an introductory survey course in physics
for science majors, is a good discussion of chiral symmetry, and
its breaking. As a single example of the complexity of the
electroweak theory, a left-handed electron is NOT the same
particle as a right-handed electron, and a left-handed positron
is NOT the same particle as a left-handed anti-electron! A
good way to summarize electroweak processes is that EVERYTHING
MIXES or is mixed. Because of the great importance of
chiral symmetry, one of the goals of relativistic heavy ion
collision studies has been and continues to be to discover if,
when a quark-gluon plasma is formed (if it is), chiral symmetry
might be briefly restored.
EMPIRICAL MASS FORMULAE FOR
QUARKS AND LEPTONS?
In the Standard
Model, masses are basically inserted “by hand,” as
free parameters, not being predicted by the theoretical
framework. As a result, beginning with Nambu back in
1952, there has been considerable interest in finding
empirical relations between the masses of the fundamental point
particles of the SM. Since the u, d and s quarks do not
get most of their mass from the Higgs field , they are usually
excluded from the quest. However, a similar equation works for
u, d and s if the mass of the u is set to zero! The
relationships seen above were published by Yohsio Koide in
1982. Accurate empirical mass formulae would be of great
utility, particularly for neutrinos, since their specific masses
are currently unknown. See also this. [And a
recent effort along
related lines by Kevin Loch.] There seem to be two main
motivations for such work: (1) an attempt to seek hints of a
sublevel below the SM, namely a constituent description of
quarks and leptons; and, (2) an attempt to seek combinations of
physical constants that appear to play a role in determining the
masses of the quarks and leptons. It is safe to say that
such efforts are not taken very seriously by the majority of
physicists. I did a quick survey of about 20 semi-recent
papers... their most distressing feature is that generally the
authors did not distinguish between current masses and
constituent masses... in other words, they didn't just fit
fundamental point lepton and quark masses (sparse data!), but
also or instead fit masses of baryons and mesons!!
Strings?