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[Phys-l] Grand Unification, SUSY and Baryogenesis.



Grand Unification, SUSY and Baryogenesis.


There are many particle physics models which attempt to explain the
creation of the all the matter in the Universe produced by re heating at the exit
of the inflation era. Nevertheless, very little is known with any
certainty and these various models remain speculative. In this post I add to this
speculation by proposing what would seem to be a very attractive model
based on Grand Unification and Super Symmetry. I make no pretense to rigor.


NOTATION


Before I start I need to explain the notation that will be used in this
post. This notation is important because it makes clear the attractive
features of this proposal. Every particle I will introduce will be defined by
this notation. This notation shall consist of helicity, electric charge, color
charge, and B-L charge. The model is based on SU(3) X SU(2)_LX U(1)_Y
symmetry. For color charge I will the notation a,b,c for color and A,B,C, for
anti color while 0 means the particle carries no color charge. So for
example an electron would look like:

e ( L,-1, 0,-1)

Or an anti d quark

dbar ( R,+1/3,A,-1/3)

Supersymmetry partners shall be identified by the symbol ~ in front of the
flavor notation. So for example a sdown quark would be

~d( 0,-/3,a,+1/3)

The zero notation indicating a scalar particle.


Grand Unification and Baryogenesis



When the original grand unification theory was first proposed it provided a
very attractive model of Baryogenesis based on quark Lepton symmetry. This
model, based on the simplest symmetry SU(5), has turned out to be
incorrect based on the non observation of proton decay which was predicted.
Nonetheless most subsequent Grand Unification models incorporate many features of
SU(5) symmetry. It is likely in my opinion, that a modified version of
this basic symmetry which incorporates Super Symmetry might be correct. A
closely related symmetry, SO(10), incorporates the SU(5) mathematical structure
and provides an interesting mechanism to explain the enigma of neutrino
mass.

However, with the discovery of inflation, GUT baryogenesis fell out of
favor. The problem was the very high mass needed for the leptoquark boson and
the predicted re heating energy scale at the exit of inflation. The expected
re heating energy was just too low. Of course any Baryogenesis before
inflation would be diluted to zero baryon density. In addition, various
Instanton-like solutions in electroweak theory suggested a washing out of
baryons.

However, there has been renewed interests in GUT baryogenesis based on the
possibility of parametric resonance during the re heat process. This
resonance has the ability to create massive particles at an energy well below the
GUT energy scale.




The Need For SUSY.


As attractive as the new version of GUT baryogenesis might be, it is my
view that if Supersymmetry is a good symmetry of nature any model of
baryogenesis must be Supersymmetric. It seems almost certain that any Baryogenesis
process occurs at a scale where SUSY is unbroken. This presents severe
problems for models of non SUSY baryogenesis and non SUSY leptogenesis.
However, leptogenesis suffers from an even greater flaw. In the leptogenesis model
B-L charge is not conserved and there is no explanation for the origin of
dark matter for which the leading candidate is the Lightest Supersymmetry
particle. ( LSP). As we shall see by incorporating SUSY in GUT baryogenesis
all these problems are eliminated. By incorporating SUSY in our GUT
baryogenesis model we have R parity conversation, B-L conservation and most
important a value of B-L charge equal to zero in the Universe.


The model


During the process of reheating, the Inflaton field decays dumping its
energy into the production of all the particles that make up the matter in our
Universe. Little is known as how this might work. In this model I will
take this process as a given. I will assume that the first particles were
created by the decay of a scalar field
which I will call the Cosmon field whose quanta will designated by the
letter C. This particles are assumed here to have an R parity of +1. While this
is speculative, it is no more speculative than any re heating process in
any other model of particle production.


It is proposed that these C quanta decay as follows.


C(,0,0,0,0)= ~ Xbar (L, +4/3, A, +2/3) + ~X (L,-4/3,a,-2/3)


OR


C(,0,0,0,0)= ~ X bar (R, +4/3, A, +2/3) + ~X (R,-4/3,a,-2/3)


OR


C(0,0,0,0) = ~Ybar (L,+1/3,A,+1/3) + ~Y (L,-1/3,a,-1/3)


OR



C(0,0,0,0) = ~Ybar (R,+1/3,A,+1/3) + ~Y (R,-1/3,a,-1/3)








Here X and Y are Spinor Super partners of the leptoquark bosons, i.e.,
the Xino and Yino quanta. Note that these quanta have-1 R parity which
conserves R parity in these decays. Also note that B-L charge is conserved and
zero. This is not true in the Leptogenesis model.

An additional important point here is that at this energy scale, given
unbroken SUSY, all the standard model particles are massless. However, it is
expected that the leptoquark particles would be massive (on the order of the
GUT scale) because they would couple to the GUT scale Higgs fields. Of
course this would seem to require massive Cosmon quanta. There is not much that
can be said about this except that it's a problem suffered by all the
models which attempt to explain the creation of particles in the early
Universe. One possible explanation is parametric resonance as proposed by Lawrence
Krauss, Mark Trodden and others. Or as yet some additional mass generation
process. This is a question that needs further work, I will not attempt to
address this question here.



I propose that the creation of these xino and wino superpartners of the
leptoquark bosons would quickly lead, based on SU (5) Symmetry, to the
following decay processes.

Channel 1


~Xbar (L,+4/3,A,+2/3)= ebar ( R,+1,0,+1) + ~dbar ( 0,+1/3,A,-1/3)



Channel 2


~Xbar (R,+4/3,A,+2/3)= U (L,+2/3,b,+1/3) + ~ U (0,+2/3,c,+1/3)


Channel 3


~Ybar( L,+1/3,A,+2/3) = vbar (R, 0,0, +1) + ~dbar ( 0,+1/3,-1/3)


Channel 4

~Ybar ( R,+1/3,A,+2/3) = U ( L,+2/3,b,+1/3) + ~ d ( 0,-1/3,c,+1/3)




And the anti leptoquark boson super partners.


Channel 5


~ X ( L, -4/3, a, -2/3)= Ubar ( R, -2/3, B, -1/3) + ~ Ubar ( 0, -2/3, C,
-1/3)


Channel 6



~ X ( R, -4/3, a, -2/3) = e ( L,-1,0,-1) + ~d (0,-1/3,,a,+1/3)


Channel 7

~Y ( L, -1/3, a,-2/3)= Ubar ( R,-2/3,B,-1/3) + ~ dbar ( 0,+1/3, C,-1/3)


Channel 8

~Y (R,-1/3, a, -2/3) = v ( L,0, 0, -1) + ~d ( 0,-1/3, a, +1/3)


Of course there are other possible decay channels such as ~v and d
particle. But this is sufficient to illustrate the process.


It should be noted that particles produced in this decay process are
massless, since these decays occur above the SUSY breaking scale. But the
leptoquark Spinors are proposed to be massive due their coupling to the GUT scale
Higgs field. This is thought to be true of the right handed singlet in SO
(10) symmetry, which is proposed to explain the very small neutrino masses.
I have not attempted to incorporate this singlet in this model. However, if
the mass of this singlet were less than the mass of the leptoquark Spinors
than anomalous decays are possible such as;


xbar ( L,+1/3, A, +2/3) = N ( R, 0, 0, +1) + ~dbar ( 0,+1/3, A, -1/3)


This would seem to pose no problem one way or the other.



An another very helpful feature of this model is that it provides an
explanation for Dark Matter. We can see that when SUSY breaks we should expect
decays such as


~ d ( 0, -1/3, a, +1/3) = d ( L, -1/3, a, +1/3) + chi ( L, 0, 0, 0)

Where Chi is the neutralino, the leading candidate for the LSP dark matter
particle. Also it should be noted that this model constrains the number of
neutrinos produced during Baryogenesis, the constrain being B-L
conservation to ensure that B-L in the Universe is zero. Of course many more neutrinos
are created by nuclear fusion in stars, but in all processes B-L charge,
no less than electric charge in conserved.



We can see here that in order to produce the slight favoritism of matter
over anti matter, the Cosmon quanta would have to experience slightly more
decays into leptoquark Spinors with right handed helicity. This can be seen
by the decay channels above where the even numbered channels produce matter
and the odd number channels produce anti matter. This can be done while
conserving all charges, including R parity and B-L charge and in a Universe
with all charges at zero. This is really quite elegant in my opinion.

Bob Zannelli