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?