Supersymmetric electroweak baryogenesis
135
Similarly, the assumption that supergauge interactions are in equilibrium implies
that
~p =~p
(4.235)
for any particle p and associated sparticle p. Intermediate between these
interaction rates are those of various inelastic processes, including those
associated with the interaction Lagrangian and 'strong sphaleron' processes. We
shall see in the following chapter that. although baryon number is conserved by
QCD, the axial baryon-number current
J~5) == LtlYIlYSq
(4.236)
q
is anomalous and there are strong sphaleron solutions, analogous to the
electroweak sphalerons, that connect different topological sectors.
Their
contribution to the coupled diffusion equations conveys the CP-violation to
all quark flavours. The rate rss of such processes is of order a~T and
comparable with those arising from the top Yukawa coupling, so they must be
included. Although neither of the foregoing assumptions is a particularly good
approximation, it is believed. or at least hoped. that they lead to multiplicative
errors of at most of order unity in the predicted baryon asymmetry.
In the analysis of [69], the sources Si of the CP-violating asymmetry arise
solely from the chargino sector. The squark sector is ineffective because, for
bosons, the CP-violating source arises only at second order in the gradient
expansion of the CP-violating mass. Charginos are mass eigenstates arising from
Higgsino-Wino mixing. However, any asymmetry from the Wino component
can only be transported to a chiral asymmetry in quarks and squarks via mixing
effects, whereas a Higgsino asymmetry is transported directly via strong Yukawa
interactions. Thus, the set of diffusion equations to be considered can be
simplified by neglecting chargino mixing and dropping any Wino contributions.
With the foregoing approximations, the number of coupled diffusion equations
is reduced to those for the two Higgsino densities ~i,1 and ~i,2' which have CPviolating sources Si,1 and Si,2' plus those for the third quark generation doublet
~q3 and the right-chiral top ~'R' and those for first- and second-generation doublets
~ql.2 and right-chiral singlets ~qR' which are coupled to the first four equations
only by strong-sphaleron interactions. The equations may be solved numerically
and the last step is to calculate the baryon asymmetry induced by weak sphaleron
effects on the CP-violating asymmetries ~i.
Since the weak sphaleron derives entirely from the SU(2)L component of
the electroweak gauge group, the baryon asymmetry results from left-chiral quark
and lepton asymmetries in front of the bubble wall. The latter are essentially zero
in this approach and the former enter the baryon-number-violating rate equation
dnB
3 (
nB)
(4.237)
Tt = 2 rb ~qL - AT2
135
Similarly, the assumption that supergauge interactions are in equilibrium implies
that
~p =~p
(4.235)
for any particle p and associated sparticle p. Intermediate between these
interaction rates are those of various inelastic processes, including those
associated with the interaction Lagrangian and 'strong sphaleron' processes. We
shall see in the following chapter that. although baryon number is conserved by
QCD, the axial baryon-number current
J~5) == LtlYIlYSq
(4.236)
q
is anomalous and there are strong sphaleron solutions, analogous to the
electroweak sphalerons, that connect different topological sectors.
Their
contribution to the coupled diffusion equations conveys the CP-violation to
all quark flavours. The rate rss of such processes is of order a~T and
comparable with those arising from the top Yukawa coupling, so they must be
included. Although neither of the foregoing assumptions is a particularly good
approximation, it is believed. or at least hoped. that they lead to multiplicative
errors of at most of order unity in the predicted baryon asymmetry.
In the analysis of [69], the sources Si of the CP-violating asymmetry arise
solely from the chargino sector. The squark sector is ineffective because, for
bosons, the CP-violating source arises only at second order in the gradient
expansion of the CP-violating mass. Charginos are mass eigenstates arising from
Higgsino-Wino mixing. However, any asymmetry from the Wino component
can only be transported to a chiral asymmetry in quarks and squarks via mixing
effects, whereas a Higgsino asymmetry is transported directly via strong Yukawa
interactions. Thus, the set of diffusion equations to be considered can be
simplified by neglecting chargino mixing and dropping any Wino contributions.
With the foregoing approximations, the number of coupled diffusion equations
is reduced to those for the two Higgsino densities ~i,1 and ~i,2' which have CPviolating sources Si,1 and Si,2' plus those for the third quark generation doublet
~q3 and the right-chiral top ~'R' and those for first- and second-generation doublets
~ql.2 and right-chiral singlets ~qR' which are coupled to the first four equations
only by strong-sphaleron interactions. The equations may be solved numerically
and the last step is to calculate the baryon asymmetry induced by weak sphaleron
effects on the CP-violating asymmetries ~i.
Since the weak sphaleron derives entirely from the SU(2)L component of
the electroweak gauge group, the baryon asymmetry results from left-chiral quark
and lepton asymmetries in front of the bubble wall. The latter are essentially zero
in this approach and the former enter the baryon-number-violating rate equation
dnB
3 (
nB)
(4.237)
Tt = 2 rb ~qL - AT2