Baryogenesis in GUTs
99
As anticipated, llB and, hence, the baryon asymmetry, vanishes if none of the X
decays produces a baryon number and if there is no C- or CP-violation. Further,
if thermal equilibrium were maintained any net baryon number produced by the
decays is cancelled by inverse decay.
The foregoing analysis presumed that the X and X decays release no entropy,
which is a poor approximation if Tdec « mx. In this case, the energy density p of
the universe is dominated by X particles. If this is converted entirely into radiation
at a reheating temperature TR given by
1r2
4
3 2 2
p:::: Px:::: nxmx = -N .. TR = -8 mprx
(4.53)
30
1r
using (4.47), then
1/4
nX = ~ TR = ~ 45m~ri
s
(
)
(4.54)
4mx
4 41r 3 N .. m1and the baryon asymmetry becomes
3 TR
1'/8 = --IlB
(4.55)
4mx
instead of (4.52). Either way, it seems that an encouragingly small amount of
CP-violation is entailed to generate an asymmetry on the scale (4.18) observed.
To see whether it is, we need to calculate II B in the various models containing
baryon number and CP non-conservation.
4.4 Baryogenesis in GUTs
Grand unified theories (GUTs) seek to unify the three separate gauge groups
SU(3), SU(2) and U(I) of the standard model in a simple group G:
G :::) SU(3) x SU(2) x U(1).
(4.56)
(See [13] for a review.) The GUT hypothesis is that above some high energy
(GUT) scale MG,
M G", > 10 15 GeV
(4.57)
G is an exact symmetry, which is spontaneously broken at the GUT scale to the
standard model, which is itself spontaneously broken at the electroweak scale. In
this way the (Iow-energy) gauge coupling strengths (aI, a2, a3) of the standard
model are all determined from the unknown (high-energy) coupling strength aG
of G, by using the renormalization group equations to 'run' between the GUT and
the electroweak energy scales. We have discussed this in some detail in [10] but
the essential point is that the evolution of the coupling strengths depends upon
the matter content of the low-energy theory. Since neither aG nor mG is known a
99
As anticipated, llB and, hence, the baryon asymmetry, vanishes if none of the X
decays produces a baryon number and if there is no C- or CP-violation. Further,
if thermal equilibrium were maintained any net baryon number produced by the
decays is cancelled by inverse decay.
The foregoing analysis presumed that the X and X decays release no entropy,
which is a poor approximation if Tdec « mx. In this case, the energy density p of
the universe is dominated by X particles. If this is converted entirely into radiation
at a reheating temperature TR given by
1r2
4
3 2 2
p:::: Px:::: nxmx = -N .. TR = -8 mprx
(4.53)
30
1r
using (4.47), then
1/4
nX = ~ TR = ~ 45m~ri
s
(
)
(4.54)
4mx
4 41r 3 N .. m1and the baryon asymmetry becomes
3 TR
1'/8 = --IlB
(4.55)
4mx
instead of (4.52). Either way, it seems that an encouragingly small amount of
CP-violation is entailed to generate an asymmetry on the scale (4.18) observed.
To see whether it is, we need to calculate II B in the various models containing
baryon number and CP non-conservation.
4.4 Baryogenesis in GUTs
Grand unified theories (GUTs) seek to unify the three separate gauge groups
SU(3), SU(2) and U(I) of the standard model in a simple group G:
G :::) SU(3) x SU(2) x U(1).
(4.56)
(See [13] for a review.) The GUT hypothesis is that above some high energy
(GUT) scale MG,
M G", > 10 15 GeV
(4.57)
G is an exact symmetry, which is spontaneously broken at the GUT scale to the
standard model, which is itself spontaneously broken at the electroweak scale. In
this way the (Iow-energy) gauge coupling strengths (aI, a2, a3) of the standard
model are all determined from the unknown (high-energy) coupling strength aG
of G, by using the renormalization group equations to 'run' between the GUT and
the electroweak energy scales. We have discussed this in some detail in [10] but
the essential point is that the evolution of the coupling strengths depends upon
the matter content of the low-energy theory. Since neither aG nor mG is known a