Supersymmetric e1ectroweak baryogenesis
133
into the symmetric phase region. The latter will interact and be slowed by other
particles approaching the wall. before eventually passing through the wall. Thus.
an accumulation of particles develops in front of the bubble wall. As a result of the
CP violation. there is a non-zero difference between the transmission coefficients
of these particles and their antiparticles across the wall of the bubble and a similar
difference between the reflection coefficients. These differences. in turn, generate
local source tenns for the net number densities associated with the particles
and. in particular. the Higgs number and axial top number. which appear in the
coupled Boltzmann equations, tending to pull the system away from eqUilibrium.
These particles are chosen because they participate in particle-number-changing
transitions in the wall that are fast compared with relevant time scales but they
carry charges that are approximately conserved in the symmetric phase. Transport
effects then generate a local excess (or deficit) of left-chiral charginos (say) over
their antiparticles ahead of the advancing bubble wall. Unsuppressed baryonnumber non-conservation in the symmetric phase then converts these densities
into a net baryon asymmetry, which is frozen as the bubble wall sweeps through,
provided that the sphaleron washout condition is satisfied.
All calculations [60-64], of nB in the symmetric phase are done using
coupled diffusion equations for the relevant number densities. which include
contributions arising from source currents generated at the bubble wall. scattering
processes involving the top quark Yukawa coupling, as well as Higgs-number and
axial-top-number-violatingprocesses in the bubble wall and broken phase. Higgsnumber and quark-number diffusion tenns are also included. There is general
agreement on the equations to be used (see (4.232» but little on how to detennine
the source currents.
We have also noted that the MSSM affords new mechanisms for satisfying
the washout condition (4.225) that are unavailable to the standard model.
Specifically. the possible existence ofa light SU(2) scalar top squark iR (a 'stop')
that interacts strongly with the Higgs field might drive the necessary reduction
in the effective three-dimensional scalar self-coupling )..3 needed to generate a
sufficiently strong first-order phase transition with a Higgs mass satisfying the
current bounds [65]. Any such scalar gives a negative contribution to A,3 at
one-loop level but a light left stop h is inconsistent with electroweak precision
measurements. Numerical calculations [65] have confinned two-loop estimates
and shown that these are even somewhat conservative. The conclusion is that there
are parts of the MSSM parameter space not excluded by experiment where the
electroweak phase transition is strong enough to allow baryogenesis. However,
besides needing a light stop m;R $ m" there must either be a much heavier stop
mh ~ 10m, or else two independent light Higgs particles mh.A $ 120 GeV. (h is
the scalar Higgs and A the pseudoscalar.)
The next question then is whether in this region of parameter space the
additional sources of CP-violation in the MSSM can generate source tenns for
the various particle densities that are strong enough to induce sufficient baryon
asymmetry in the symmetric phase. which is then frozen in as the bubble wall
133
into the symmetric phase region. The latter will interact and be slowed by other
particles approaching the wall. before eventually passing through the wall. Thus.
an accumulation of particles develops in front of the bubble wall. As a result of the
CP violation. there is a non-zero difference between the transmission coefficients
of these particles and their antiparticles across the wall of the bubble and a similar
difference between the reflection coefficients. These differences. in turn, generate
local source tenns for the net number densities associated with the particles
and. in particular. the Higgs number and axial top number. which appear in the
coupled Boltzmann equations, tending to pull the system away from eqUilibrium.
These particles are chosen because they participate in particle-number-changing
transitions in the wall that are fast compared with relevant time scales but they
carry charges that are approximately conserved in the symmetric phase. Transport
effects then generate a local excess (or deficit) of left-chiral charginos (say) over
their antiparticles ahead of the advancing bubble wall. Unsuppressed baryonnumber non-conservation in the symmetric phase then converts these densities
into a net baryon asymmetry, which is frozen as the bubble wall sweeps through,
provided that the sphaleron washout condition is satisfied.
All calculations [60-64], of nB in the symmetric phase are done using
coupled diffusion equations for the relevant number densities. which include
contributions arising from source currents generated at the bubble wall. scattering
processes involving the top quark Yukawa coupling, as well as Higgs-number and
axial-top-number-violatingprocesses in the bubble wall and broken phase. Higgsnumber and quark-number diffusion tenns are also included. There is general
agreement on the equations to be used (see (4.232» but little on how to detennine
the source currents.
We have also noted that the MSSM affords new mechanisms for satisfying
the washout condition (4.225) that are unavailable to the standard model.
Specifically. the possible existence ofa light SU(2) scalar top squark iR (a 'stop')
that interacts strongly with the Higgs field might drive the necessary reduction
in the effective three-dimensional scalar self-coupling )..3 needed to generate a
sufficiently strong first-order phase transition with a Higgs mass satisfying the
current bounds [65]. Any such scalar gives a negative contribution to A,3 at
one-loop level but a light left stop h is inconsistent with electroweak precision
measurements. Numerical calculations [65] have confinned two-loop estimates
and shown that these are even somewhat conservative. The conclusion is that there
are parts of the MSSM parameter space not excluded by experiment where the
electroweak phase transition is strong enough to allow baryogenesis. However,
besides needing a light stop m;R $ m" there must either be a much heavier stop
mh ~ 10m, or else two independent light Higgs particles mh.A $ 120 GeV. (h is
the scalar Higgs and A the pseudoscalar.)
The next question then is whether in this region of parameter space the
additional sources of CP-violation in the MSSM can generate source tenns for
the various particle densities that are strong enough to induce sufficient baryon
asymmetry in the symmetric phase. which is then frozen in as the bubble wall