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Charge Quantification and The Standard Model



Dear List Members:
What follows is a presentation of some of the work of the Indian
Physicist Afsar Abbas of the Institute of Physics, Bhubanewar India. It is my
opinion that Dr. Abbas has made some important points. His basic point is
that the Standard Model is telling us something interesting about nature that
we are not paying attention to. When the SM and the various TOEs disagree, he
opts for the experimentally verified standard model. I am in communication
with Dr. Abbas and he has graciously consented to answer any questions anyone
may have. However, if list members find my presentation interesting I hope
they will take the time to read his papers which are available in the LANL
archive.


Charge Quantification and The Standard Model

As the Universe expands, after the "creation" event it is predicted that it
will undergo a series of phase transitions. It is believed that at high
temperatures the group structure which correctly describes the symmetries of
nature is

SU(N_c)XSU(2)_LX(U1)_Y

At approximately T=1TEV (after approximately 1E_10 seconds) the universe
undergoes the breaking of electroweak symmetry, induced it is believed, by
what has been called the Higgs mechanism. The Higgs mechanism is a prediction
that a scalar field interacts with the particles of the standard model,
causing them to acquire mass. This breaks the chiral symmetry associated
with the Fermions by giving each fermion a non zero right spin probability
amplitude (and every antifermion a non zero left spin probability amplitude).

Most importantly for the purposes of this post, the breaking of
electroweak symmetry by the Higgs field transforms the fundamental parameters
of the SM, weak isospin and weak hypercharge into the symmetry structure we
see today.

SU(N_c)_cXU(1)_em

Before the EW symmetry breaking, the quanta associated with each one
of these gauge fields were massless. After the effect induced by the Higgs
field the isospin breaks to two massive charged quanta and two orthogonal
mixtures with the hypercharge field to create the electromagnetic field and
the neutral weak field. Of these two, only the electromagnetic field retains
a massless state. These fields are quantified by the W+, W-, Z0 and photon
particles of the Standard Model.
This scenario, which is well supported experimentally, may have
consequences which have been overlooked. For example, it is commonly believed
that electric charge quantization must be put in by hand in the SM and some
form of Grand Unification Theory is needed above the electroweak scale to
explain electric charge quantification. This, is fact, is considered one of
the successes of SU(5) or SO(10) models. However since the SM doesn't allow
for a U(1)_em symmetry above the electroweak scale we may have reason to
question this point.
Afsar Abbas proposes that in fact we can insure the quantification of
electric charge by just using considerations inherent in the SM. Let us
consider the SM structure looking at just the first generation of Fermions.
We have.

q_l= { u, d } ( N_c, 2 ,Y_q)

u_r (N_c,1, Y_u)

d_r (N_c, 1, Y_d)

L_L= {e, mu} (1.2,Y_L)

e_r (1,1,Y_e)

At this point we have five unknown hypercharges. (Note here we take the
neutrinos as massless which is only approximately correct.) In the SM model
we define electric charge by

Q'=a"*I_3+b'*Y

where a' & b' are terms of the diagonal generators of SU(2)_LXU(1)_Y
Commonly we scale these such that Q=Q'/a' & b=b'/a' so that we get

Q=I_3+b*Y

In the SM the Higgs is assumed to be a doublet "theta" with an arbitrary
hypercharge Y_theta. We also label the Higgs isospin component T_3. In the
SM. the following relationship holds for electric charge.

Q=T_3-(T_3/Y_theta)*Y

Because Q_L=Q_R and right spinning Fermions have zero isospin in the
standard model we get

Y_u=Y_q-Y_theta/(2*T_3)

Y__d=Y_q+Y_theta/(2*T_3)

Y_e=Y_L+Y_theta/(2*T_3)

And to insure the cancellation of triangle anomalies we get

Y_l=Y_theta/(2*T_3)

Y_q=-Y_theta/(2*T_3*N_c)

From this we can see that
Q(u)=(1/2)*(1+(1/N_c))

Q(d)=(1/2)*((1/N_c)-1)

Q(e)=-1 ( N_c=1)

Q(mu)=0 ( N_c=1)

(In the Universe today we have good experimental support for N_c=3 for
quarks)

Note that we have quantized the electric charge using just SM
consideration alone. Also this is true for any arbitrary Higgs isospin and
hypercharge. Therefore as far as charge quantization goes the values T_3 and
Y_theta remained unconstrained. ( However Y_theta=-2*T_3)
Let us look at the weak and electromagnetic neutral currents with
this point in mind. In the SM we have A_mu the neutral EM vector potential
and Z_mu the neutral weak current vector potential which are orthogonal to
each other and are derived from the mixing of the orthogonal isospin and
hypercharge terms.

A_mu=g_2*B_mu+g_1*(2*T_3?Y_theta)Y_L)*W_mu/

sqrt[g_2^2+(g_1*(2*T_3/Y_theta)*Y_L]

Z_mu= -g_2*(2*T_3/Y_theta)*Y_l*B_mu+g_2*W_mu/
sqrt[g_2^2+(g_1*(2*T_3/Y_theta)*Y_L]

Given that Y_l=Y_theta/(2*T_3) and g_1=e*sec[theta_w] & g_2=e*csc[theta_w]

where e is the electric charge of the electron and theta_w is the
weak mixing angle. This agrees with the electroweak formulation

U*{ W_0, B_^0}={Z_0, A_0}

Where U_11=cos[theta_w] U_12=-sin[theta_w]
U_12=sin[theta_w] U_22=cos[theta_w]

Which gives the well known equations for neutral weak and neutral EM current
respectively.

Z_0=W_0*cos[theta_w]-B_0*sin[theta_w]

A_0= W_0*sin[theta] + B_0*cos[theta_w]

So we see that we can generate the proper symmetries of the SM without
defining specific vev values for the Higgs field. We also see that contrary
to general physics lore, the SM does require electric charge to be quantized.
Also we can see that electric charge is a function of the color degrees of
freedom and that we can avoid triangle anomalies for any value of N_c as long
as we abide by the quantization of electric charge demanded by the SM.
In addition, the full structure of the SM. remains intact without
constraining the hypercharge of the Higgs field to any specific value. All
particles in the lab have exact Quantum numbers which defines their identity.
However all the hypercharges of the SM particles are rooted in the vev of the
Higgs hypercharge, which itself remains free and unspecified. This has led
Abbas to the notion that the Higgs field may not in fact be quantified and
may just be a measure of the vacuum which sets up the whole SM structure. If
this is true we will never see a Higgs particle in our labs.
There are other even more controversial implications of this line of
reasoning. They are not likely to be easily accepted given the current
directions in physical theorizing. However since in science we shouldn't
haven't sacred cows these ideas are worth some consideration.

Superstring Theory and Quantum Gravity
Implications

In Superstring Theory the property of electric charge is postulated to exist
right up to the Planck scale. In Superstring theory there are always color
neutral fractionally charged particles unless certain parameters are
constrained. However to constrain these values to eliminate color neutral
fractionally charged particles would require that SU(3)XSU(2)XU(1) never
breaks symmetry which is observationally falsified.
Based on this, Superstring theorists have two options. Predict
observable color neutral fractionally charged particles, which are unlikely
given current experimental results, or predict that these fractionally
charged particles acquire sufficient mass to be out of the reach of
observation. Superstring theorists generally opt for the latter explanation.
However given the lack of observational support for Superstring theory in
general, this explanation seems unconvincing to me. Also we have seen that
electric charge is necessarily quantified as a function of N_c in the
standard model. This would strictly prohibit color neutral fractionally
charged particles. Again we have a direct contradiction between the SM and
Superstring theory. While the SM is well supported by experiment, Superstring
theory has yet to produce one correct experimental prediction. Therefore a
resolution of these contradictions would seem to favor the SM prediction! .
In addition their are other more startling consequences of
Abbas's theory. Since in his theory we lose U(1)_em symmetry above the
electroweak scale, it seems difficult to understand it what sense we can have
electric charge at energies greater than approximately 1 TEV. Once it is
accepted that above the EW scale particles have "forgot" their electric
charge and an orthogonal mixture of weak hypercharge and isospin no longer
exist to create an EM field, then it would seem the basic space-time metric
could not exist in it's current form. This is because

C^2=1/mu_0*eplison_0

Where eplison_0 is the vacuum permittivity and mu_0 is the vacuum
permeability. These electromagnetic properties would disappear along with
electric charge above the EW scale and hence the velocity of light also
disappears as a fundamental constraining parameter in the Universe. Note that
the equation for the SR invariant interval is.

S^2=(c*t)^2-x^2-y^2-z^2

Based on this we can see that c provides us with a means of defining time in
terms of spatial separation and visa versa. Therefore it would seem that
above the electroweak scale, there is no time as we know it. Hence it would
seem that the creation of the lorentz invariant space-time metric comes into
existence at the EW scale. Above this scale, we may well expect the Universe
to be in a state similar to the one predicted by the Hawking-Hartle no
boundary theory.
This would also mean that SM particle Quantum numbers and Fermion family
replication would both occur at the EW breaking scale. This has clear
implication for Gerald's theory as well as does the electric charge structure
predicted by Abbas.
Also it should be noted that these ideas would provide a unique and
perhaps philosophically satisfying answer to the hierarchy problem. That is,
the so called desert of new physics between the EW and Planck scale. In
addition this idea may provide an explanation of why theories at or near the
Planck scale suffer the contradiction of highly ordered structure and
predicted Quantum chaos.
Abbas's theory certainly represents a paradigm shift in current
physical theorizing. For that reason it not likely to easily get a place at
the table of ideas. However this theory is based in principal on the highly
successful SM, the only Quantum theory which has made direct contact with
experiment. All other theories beyond the SM have yet to either make any real
prediction (Superstring theory) or to have any of their predictions (Quantum
Gravity) verified to be correct. Therefore it is my opinion that this unique
and original approach deserves serious consideration.

Bob Zannelli

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.