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.




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?