4.6 Beyond the Standard Model 211asymmetry and the possibility of its dynamical generation becomes an inevitable
element of inflationary cosmology. Theories beyond the Standard Model provide us
with many−perhaps too many−potential solutions to this problem. Fortunately,
any particular model for baryogenesis should possess three basic ingredients which
are independent of the details of the actual theory. These ingredients, formulated
by A. Sakharov in 1967, are
(i)baryon number violation,
(ii)CandC P violation,
(iii)departure from equilibrium.
The first condition is obvious and does not require a long explanation. If baryon
number is conserved and is equal to zero at the beginning, it will remain zero forever.
If baryon number does not satisfy any conservation law, it vanishes in the state of
thermal equilibrium. Therefore we need the third condition. The second condition
is less trivial: it is a prerequisite for ensuring a different reaction (decay) rate for
particles and antiparticles. If this condition is not met, the numbers of baryons and
antibaryons produced are equal and no net baryon charge is generated even if the
other two conditions are fulfilled.
Problem 4.32Why must we require bothCandCPviolation? Why isCPviola-
tion alone not enough?
The Standard Model possesses all the ingredients necessary for the generation
of baryon asymmetry. In fact, we have seen that baryon number is not conserved
in topological transitions,CPis violated in weak interactions and the departure
from thermal equilibrium naturally occurs in the expanding universe. It would be
remarkable if the baryon number could be explained within the Standard Model
itself. Unfortunately this seems not to work. The main obstacle is the third condition.
For realistic values of the Higgs mass, the electroweak transition is a cross-over and
cannot supply us with the necessary strong deviations from thermal equilibrium.
Therefore, to explain baryon asymmetry we have to go beyond the Standard Model.
There is a wide range of possibilities; below we outline the baryogenesis scenarios
most commonly considered.
Baryogenesis in Grand Unified TheoriesBaryon number is generically not con-
served in Grand Unified Theories. In theSU( 5 )theory, for example, the heavy
gauge bosonX,responsible for “communication” between the quark and lepton
sectors, can decay into either aqqpair or aq ̄ ̄lpair with baryon numbers 2/3or
− 1 /3 respectively. The antibosonX ̄decays into aq ̄q ̄orqlpair. TheCPTinvariance
requires the equality of thetotaldecay rates forXandX ̄.However, this does not
mean that the decay rates are equal for every particular channel. IfCandCPare