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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