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[Phys-L] The Parity Issue.

A fine tuning issue you don't hear much about is related to the fact that
exhaustive searches for parity violation in the Electromagnetic interaction
has failed to find any. The reason this is surprising is because the
electroweak unification theory reveals the intimate relationship between the EM and
the weak force. To illustrate why this seems to imply fine tuning I will
briefly describe this relationship in the simplest terms possible.

We believe that the weak and electromagnetic fields are the results of
mixtures of other fields in existence at higher energies. That is at higher
energy we have

SU(2)_L X U(1)_Y symmetry with the left handed component being W(1) W(2)
W(3) and U(1) hypercharge field Y .



The fields we see at lower energy are mixers of these fields where

U( phi)= EXP[ i*theta*sigma_y] which is 2 x 2 unitary mixing
matrix.

So that

{ A_mu, Z_mu} = U(theta_w)* { A_Y W(3)_L}

and { W(+)_L W(-)_L} = U(-45 degrees) *{ W(1)_L W(2)_L }

Where theta_w is the weak mixing angle ( also known as the Weinberg angle)


Giving us

SU(2)_w X U(1)_em

Therefore

A_mu= cos(theta_w)* A_Y + sin(theta_w)* W(3)_L.


Z_mu= -sin(theta_w) A_Y + cos(theta_w)* W(3)_L

We know the neutral component of the weak interaction ( Z_mu) has a 15
percent or so higher probability of coupling with left handed polarized beam of
electrons than an un-polarized beam of electrons. This indicates a strong
preference for the weak neutral field to couple to left handed fermions ,
which is not surprising given its approximately 77 percent left handed component.
However, for the electromagnetic interaction we see not the slightest
hint of any left handed ( or righted handed ) preference. This is perhaps
surprising because we know from the equation above that the EM field has about a
23 percent left handed component.
This must mean that the hypercharge field must have a compensating right
handed component which exactly balances the left handed component from the
W(3)_L field. Such fine tuning is very suspicious and probably indicates a
symmetry is involved in conserving parity for the EM interaction. This symmetry
is likely time symmetry. ( We may be seeing the same effect in particle
exchange amplitudes where the only observable states are the two special cases ,
Fermi Dirac and Bose-Einstein statistics)

The above considerations would seem to favor an unbroken left right symmetry
at higher energies perhaps suggesting the Pati Salam group structure.


SU(4)_ps X SU(2)_L X SU(2)_R

TO SU(3)_c X SU(2)_L X SU(2)_R X A_B-L

TO SU(3)_c X SU(2)_L X U(1)_Y

This group structure suggest


{ A_Y Zprime} = U(theta_z)*{ A_B-L , W(3)_R}


( W(+)_R W(-)_R } U( -45 degrees)* { W(1)_R W(2)_R}

Where theta_z is a new mixing angle, the Zprime angle.


This gives us a new neutral particle and two additional charged particles.
From the symmetries above we would expect the new boson to couple to weak
hypercharge rather than weak isospin and we would expect to see the same
electric charges for the right handed charged bosons.

W= { T3_L A_Y}



W(+)_L = { 1 0} W(-)_L = { -1 0} W(+)_R = { 0 2} W(-)_R={0
-2}


Where

A_Y= cos(theta_z)* A_B_L + sin(theta_z)* W(3)_R

Zprime= - sin(theta_z)*A_B_L + cos(theta)*W(3)_R


Assuming this is the structure nature used , than to exactly balance left
and right symmetry for the EM interaction

theta_z=arcsin[ tan(theta_w)]

Of course other symmetry structures are possible , this represents the most
straight forward version. So why are these mixing angles so fined tuned? Is
it time symmetry that restricts TSI violation to the weak interaction? (
Apparently) If these two mixing angles weren't so fine tuned would the photon
couple to the Higg's interaction? This would give us a very different
Universe indeed. These seem like important and interesting questions.

Bob Zannelli
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