Natural Science Forum / Physics / Research / February 2005

... as for most people, nowadays; to avoid spammers.

Take a look at the SU(3) sector.  The top quark has a mass around
170-175 GeV, which is on the order of the V parameters.  Given that the
strong coupling constant g_s is near 1, there may also be a fit to (sum
of quark masses) = V g_s^2 or something of the like.

A nice heuristic can be found in classical theory.  One thinks of the
electron as having a capacitance C given by the classical relation
Energy = Charge^2/C.  Then, C will be related to the charge by C =
e^2/(2 mc^2).

This basically resurrects Maxwell's theory of vacuum polarization and
the vacuum dielectric (not as well-known nowadays, though present in
his treatise); these closely foreshadowed the developments that
proceeded following the emergence of renormalization theory (including
the screening argument).  The corresponding breakdown voltage, here,
would be e/C = 2 mc^2/e, or 1.022 MV.  So, one can think of the pair
annihilation as being the breakdown of the vacuum dielectric.  The
total energy of the total charge e going across this potential is 1.022
MeV, which is precisely what's released in the form of photons
(Maxwell's "glow").

If you're going to invoke the idea of lepton number, then it almost
certainly has to be in the combination (Baryon - Lepton), the "5th
force" famous from the 1980's.  This is the only other
generation-independent charge that can be added consistently to the
SU(2) and SU(3) sectors, with the given fermion spectrum.

The argument, if you're not familiar, rests in perturbation theory,
requiring that the anomaly corresponding to the triangle diagram (3
fermion lines in a triangle, boson lines coming off of it), cancel.
This, in turn, imposes severe restrictions on whatever Yang-Mills
theory is being used, to the effect:
               Tr(gamma_5 Y_a Y_b Y_c) = 0
where Y_a, Y_b, Y_c are any gauge generators.

For SU(2) and SU(3), this automatically works.  For the Standard Model,
the only other charge that will work with this is the electric charge.

If one extends the standard model to allow for 4-component neutrinos,
then the results open up a bit.  The only charge allowed by the
condition is then a combination of electric charge and (Baryon -
Lepton).

The places where this "5th force" would have effect are: a slight
differential in the gravitational behavior of atoms, since an atom's
5th force charge will just be its neutron number.  Isotopes will then
have a slightly different behavior (though whether this or anything
else will be measurable is an entirely different matter).  Matter and
anti-matter will behave slightly differently.  It will affect neutron
star physics.  If the force, on the other hand, is only short range,
then all these effects will be correspondingly harder to find, and the
question will then become what the mass of the corresponding boson is.

The paper is way too long, as others have pointed out.  It should not
take 100 pages to explain that adding a chiral mass term to the
electroweak sector of the leptonic part of the standard model results
in a theory whose requirement for consistency imposes constraints on
the mass spectrum that closely match the actual masses seen.  That's 20
pages at most.  There's too much in the paper that's way too elementary
that's supposed to already be assumed as background and not be spelled
out.