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Re: [Phys-l] CP Violation and the Equivalence principle



Hi-
Are you referring to the following published paper? If so, have you checked out the citations to it?
Phys.Lett.B282:256-262,1992
Regards,
Jack


On Mon, 10 Jul 2006 Spinoza321@aol.com wrote:

A topic of great interest to me is the role of time symmetry (and time
asymmetry) in Quantum theory.


There is one micro arrow of time which cannot be disputed. This is of course
the arrow of time associated with CP violation. Penrose, Zeh , Davies and
others have all come to the conclusion that any "master arrow" of time must
have gravity at its origin. This may also apply to the arrow of time associated
with CP violation.

G. Chardin of the Centred'Etudes de Saclay and J-M Rax of Princeton
University have written a very interesting paper.( I will make available upon
request.)

This paper proposes that CP violation results from the break down of the
Equivalence Principle in Quantum gravity. As is well known , Super gravity and
supersymmetry theories predicts this will occur. However more specific to CP
violation is the differences of matter and anti matter (Which may swaps across
the quark lepton sector) in a Quantum theory of gravity which incorporates
super symmetry in one form or another. So I thought it might be interesting to
look at how supersymmetry modifies gravity theory.


Basically when we expand gravity into the Quantum realm by incorporating
supersymmetry we get two new gravity fields. These are


Graviscalar field.

This field is mediated by the graviscalar field and couples to what I
will call scalar mass. Interesting scalar mass is not a Quantum charge but like
tensor field related mass has any range of continuous values. Also the scalar
mass is less for a bound system so for example a gram of hydrogen would have
more scalar mass than a gram of iron. We might perhaps define scalar mass as

M_scalar= 2*M_inertial-SUM {all constituents} m_ constituents

Where m is the tensor gravity mass.


Graviphoton field

Here this gravity field is mediated by a vector particle we call the
graviphoton. This field must couple to Quantum charges which at low energy are
essentially global. In my opinion the obvious candidate is the B-L charge which is
likely conserved up to the GUT scale and maybe beyond and is postulated to be
gauged at high energy by the Pati Salam symmetry proposal.



Gravitensor

And of course we have the gravity mediated by the spin 2 graviton.


The potential equation for these fields takes the form


V= G_s*M_1s*M_2s/R*( exp [- M_b*c*R/hbar])

Where M_s and G_s are the particular mass charges and spin related
coupling factors and M_b is the tensor mass of the related boson mediating this
gravity interaction. Of course for the tensor gravity potential M_b=0 so this
reverts back to the classic form. The expected mass ranges for the graviphoton
and graviscalar are expected to be approximately in the TEV range which is
near or at the EW symmetry breaking scale.

In the paper linked , epsilon the CP violating parameter is related to the
expected gravity related "regeneration" time and is found to be in good
agreement with mixing time imposed by the weak interaction for the kaon system.


Basically CP violation occurs in the Kaon system by the mixing of "majorana"
like kaon states called K_1 and K_2.


We get

K_0= [d sbar> and K_0bar= [ dbar s>


K_1= (1/sqrt2)* [ K_0 - K_0bar> and K_2=(1/sqrt2)*[ K_0+K_0bar]


Therefore (these are Psuedoscalar particles)

CP[K_1>=K_1> and CP[K_2>= - [K_2>


It is the mixing of CP odd and CP even states that generates the observed CP
violation which gives the long decay and short time decay states which have a
finite amplitude for the other decay mode.


{ K_s K_L } =M* {K_1 K_2 }


Where

M_11=1/sqrt[ 1+epsilon ^2] M_12= - epsilon /
sqrt[1+epsilon^2]


M_21= epsilon / sqrt[1+epsilon^2] M_22= 1/sqrt[ 1+epsilon
^2]



Finally I might just mention the interesting case of the strong interaction
which is believed to need the scalar Peccei-Quinn field to avoid a similar
time asymmetry.


What makes all this interesting I think or actually one of the things that
make this interesting is the possibility of a significantly larger micro time
asymmetry in the Universe prior to the breaking of the PQ symmetry and
Supersymmetry. One might speculate that this would generate a large cosmological
constant due to ZPE effects and provide an inflationary mechanism that
utilizes the cosmological constant. When these symmetries broke we might assume
that they suppressed the cosmological constant to its current tiny value which
might explain the acceleration of the Universe we see today. well MAYBE.


Bob Zannelli




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