4.6 Beyond the Standard Model 215coincide with the flavor (weak) eigenstates. These states are related by the cor-
responding Kobayashi–Maskawa mixing matrix. This naturally explains neutrino
oscillations and generically leads tocomplexYukawa couplings which are a source
ofCPviolation. As a result the decay rates
(N→lφ)=^12 ( 1 +ε)tot,(
N→ ̄lφ ̄)
=^12 ( 1 −ε)tot (4.229)are different by the parameterε 1 ,which measures the amount ofCPviola-
tion. The final products have different lepton numbers and the mean net lepton
number from the decay of theN neutrino is equal toε.Heavy neutrinos can be
produced after inflation, either in the preheating phase or after thermalization. Sub-
sequently, their concentration freezes out and the lepton asymmetry is produced in
out-of-equilibrium decays of heavy neutrinos. In the topological transitions which
follow, this asymmetry is partially transferred to baryon asymmetry in an amount
given by (4.223). Detailed calculations show that for the range of parameters sug-
gested by the measured neutrino oscillations, one can naturally obtain the observed
baryon asymmetry via leptogenesis. At present this theory is considered the leading
baryogenesis scenario.
Other scenarios In addition to Grand Unified Theory baryogenesis and leptogene-
sis there exist other mechanisms for explaining baryon asymmetry. Supersymmetry
in particular opens a number of options. Since supersymmetry extends the particle
content of the theory near the electroweak scale, the possibility of a strong elec-
troweak phase transition cannot yet be completely excluded. This revives the hope
of explaining baryon asymmetry entirely within the MSSM.
Another interesting consequence of supersymmetry is found in the Affleck–Dine
scenario. This scenario is based on the observation that in supersymmetric theories
ordinary quarks and leptons are accompanied by supersymmetric partners−squarks
and sleptons−which are scalar particles. The corresponding scalar fields carry
baryon and lepton number, which can in principle be very large in the case of a
scalar condensate (classical scalar field). An important feature of supersymmetry
theories is the existence of “flat directions” in the superpotential, along which the
relevant components of thecomplexscalar fieldsφcan be considered as massless.
Inflation displaces a massless field from its zero position (see Chapters 5 and 8)
and establishes the initial conditions for subsequent evolution of the field. The
condensate is frozen until supersymmetry breaking takes place. Supersymmetry
breaking lifts the flat directions and the scalar field acquires mass. When the Hubble
constant becomes of order this mass, the scalar field starts to oscillate and decays.
At this timeB,LandCPviolating terms (for example, quartic couplings
λ 1 φ^3 φ∗+c.c.and λ 2 φ^4 +c.c.