130
Baryogenesis
This gives
T*
0.71 < < 0.88
(4.224)
Tc
corresponding to the bounds (4.194). Thus the sphaleron-induced baryon-number
non-conserving processes with which we are concerned are not decoupled until
the temperature is well below Tc but still well above mw [51] and. at these
temperatures. the exponential suppression essentially turns off the baryon-number
production. At the higher temperatures where the Boltzmann suppression is
evaded. the rate exceeds the universal expansion rate and the resulting thennal
equilibrium washes out any baryon asymmetry. So the picture we have is as
follows: As the temperature drops below Tc, the symmetry breaks and the field
t/I develops a non-zero YEY at the minimum of the potential, as in figure 2.1.
At each point in space thennal fluctuations perturb the field t/I which then 'rolls'
classically to the new value at the global minimum. If this phase transition is
second order or a continuous crossover, the slow rolling to the new minimum
means that the departure from thermal equilibrium is too small until T drops
below T* but by then the sphaleron-induced baryon production has been turned
off by the Boltzmann exponential suppression.
Thus, the only possibility is that the phase transition is first order. In this
case, as discussed in section 2.9, for temperatures T > Tit the only minimum
of Veff is with the system in the symmetric. unbroken phase characterized by
zero YEY. As the temperature falls below Tt, a local minimum of Veff develops,
separated by a potential barrier from that at zero VEY, and below the critical
temperature (T < Td this broken phase becomes the global minimum, see
figure 2.2. Nucleation of the broken phase proceeds by the formation of bubbles
of this true vacuum in the sea of false (symmetric phase) vacuum. At some
supercooled temperature below Tc, the size of the bubbles becomes large enough
for them to overcome the surface tension effects and they expand to fill the whole
of space and complete the phase transition. Finally. for temperatures below To,
the local minimum at zero VEY disappears and only the broken phase is stable.
A baryon asymmetry may be generated as the wall of an expanding bubble
passes through a region containing particles in the unbroken phase. The Higgs
field changes rapidly because of the wall motion. as do other fields. and these
interact with the particles giving concentrations quite far from eqUilibrium. If the
baryon-number non-conserving processes and the CP-violating processes both
occur in or near the wall, a net non-zero baryon asymmetry can result: this
scenario is called local baryogenesis [52, 53]. After the wall has passed the
region we are discussing is in the true (broken phase) vacuum with v(T) #- 0,
so it is important that, in this phase, the sphaleron-induced. baryon-number nonconserving processes are turned off by the Boltzmann suppression. so that any
baryon asymmetry produced during the non-equilibrium era is frozen in. The
condition for this to happen is [50]
v(Tc) > I
(4.225)
T "" •
Baryogenesis
This gives
T*
0.71 < < 0.88
(4.224)
Tc
corresponding to the bounds (4.194). Thus the sphaleron-induced baryon-number
non-conserving processes with which we are concerned are not decoupled until
the temperature is well below Tc but still well above mw [51] and. at these
temperatures. the exponential suppression essentially turns off the baryon-number
production. At the higher temperatures where the Boltzmann suppression is
evaded. the rate exceeds the universal expansion rate and the resulting thennal
equilibrium washes out any baryon asymmetry. So the picture we have is as
follows: As the temperature drops below Tc, the symmetry breaks and the field
t/I develops a non-zero YEY at the minimum of the potential, as in figure 2.1.
At each point in space thennal fluctuations perturb the field t/I which then 'rolls'
classically to the new value at the global minimum. If this phase transition is
second order or a continuous crossover, the slow rolling to the new minimum
means that the departure from thermal equilibrium is too small until T drops
below T* but by then the sphaleron-induced baryon production has been turned
off by the Boltzmann exponential suppression.
Thus, the only possibility is that the phase transition is first order. In this
case, as discussed in section 2.9, for temperatures T > Tit the only minimum
of Veff is with the system in the symmetric. unbroken phase characterized by
zero YEY. As the temperature falls below Tt, a local minimum of Veff develops,
separated by a potential barrier from that at zero VEY, and below the critical
temperature (T < Td this broken phase becomes the global minimum, see
figure 2.2. Nucleation of the broken phase proceeds by the formation of bubbles
of this true vacuum in the sea of false (symmetric phase) vacuum. At some
supercooled temperature below Tc, the size of the bubbles becomes large enough
for them to overcome the surface tension effects and they expand to fill the whole
of space and complete the phase transition. Finally. for temperatures below To,
the local minimum at zero VEY disappears and only the broken phase is stable.
A baryon asymmetry may be generated as the wall of an expanding bubble
passes through a region containing particles in the unbroken phase. The Higgs
field changes rapidly because of the wall motion. as do other fields. and these
interact with the particles giving concentrations quite far from eqUilibrium. If the
baryon-number non-conserving processes and the CP-violating processes both
occur in or near the wall, a net non-zero baryon asymmetry can result: this
scenario is called local baryogenesis [52, 53]. After the wall has passed the
region we are discussing is in the true (broken phase) vacuum with v(T) #- 0,
so it is important that, in this phase, the sphaleron-induced. baryon-number nonconserving processes are turned off by the Boltzmann suppression. so that any
baryon asymmetry produced during the non-equilibrium era is frozen in. The
condition for this to happen is [50]
v(Tc) > I
(4.225)
T "" •