Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 86
3 The EW phase transition
The first phase transition predicted by the SMPP is the EW phase transition
which occurs at a temperature TEW ∼ 100 GeV and at a time scale
tEW ∼ 10 −10 s (e.g. Unsöld & Bascheck, 2002). At this temperature, which
corresponds to an energy scale of the order of the masses of the Z 0 and W ±
vector bosons (cf. Table 6), the weak interactions become short ranged after
a symmetry breaking phase transition. For T < TEW the Z 0 and W ± vector
bosons acquire masses through the Higgs mechanism while the photon remains
massless, corresponding to the unbroken symmetry of the electromagnetic interactions
(e.g. Boyanovsky et al., 2006).
The value of TEW was estimated considering that the restoration of symme-
try would happen when T ∼ G −1/2
F where GF ≈ 1.16637 × 10 −5 GeV −2 (e.g.
Stuart, 1999) is the Fermi coupling constant (e.g. Gynther, 2006).
In the EW standard model (Glashow–Salam–Weinberg model) the Higgs field
is responsible for the dynamical mass generation via spontaneous symmetry
breaking. At sufficiently high temperatures, T > TEW, the expectation value of
the Higgs field is zero, i.e., the symmetry is restored and particles are massless.
At T < TEW the symmetry breakes and particle masses become finite (e.g.
Kämpfer, 2000). During this transition, according to the SMPP, all particles
except the Higgs acquire their mass by the mechanism of spontaneous symmetry
breaking (e.g. Schwarz, 2003).
Csikor et al. (1998) obtained, using a nonperturbative analysis, that the
phase transition is of first–order for Higgs masses less than 66.5±1.4 GeV while
for larger Higgs masses only a rapid crossover is expected (see Figure 34). This
value must be perturbatively transformed to the full Standard Model yielding
72.4 ± 1.7 GeV (Csikor et al., 1998). The exact determination of this critical
Higgs–mass value, mH,c, at which the first–order EW phase transition changes
to a crossover is important given its implications for the standard model (e.g.
Karsch et al., 1996).
The location of the endpoint of the first–order phase transition line is seen
to move to smaller values of the Higgs mass as the chemical potentials µ are
increased, indicating that the chemical potentials make the transition weaker.
At the same time, the critical temperature is slightly increased. The value
mH,c ≈ 72 GeV corresponds to the case µ = 0. If, for example, µ ≈ 30 GeV
then we have mH,c ≈ 66 GeV (e.g. Gynther, 2006).
Both the QCD and the EW theories contain a phase transition. The exact
properties and critical temperatures of the transitions depend on the chemical
potentials and the values of parameters of the theories. The EW phase diagram
is considered in terms of the leptonic chemical µL potentials and the theory is
parametrized by the Higgs mass, while the QCD phase diagram is considered in
terms of the baryonic chemical potential µB and the theory is parametrized in
terms of the strange quark mass. When the masses parameterizing the theories
are small we have for both cases a first–order phase transition. However, as
the chemical potentials are increased, the critical temperature of the EW phase
transition increases, while the critical temperature of the QCD phase transition