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

[Spinoza321@aol.com]

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
===============================
 
 
Thanks Jack I will check this out.
 
Bob Zannelli 
 
============




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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