Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 56
which gives 2 × 4 degrees of freedom. Each neutralino contributes with two degrees
of freedom corresponding to two possible helicity states and each chargino
contributes with four degrees of freedom (two charges × two helicity states).
In order to account for these extra degrees of freedom we replace equation
(104) by the more general
g(T )=
bosons
+
sfermions
gi(T )+ 7
8
gi(T )+ 7
8
fermions
bosinos
gi(T )+
gi(T ).
(109)
At very high temperatures when all the particles contribute to the effective
number of degrees of freedom we have, according to equation (109)
g(T )=gγ + g W ± ,Z 0 + gg + gH + 7
8 [ ge,µ,τ + gν + gq ]+
+ g˜e,˜µ,˜τ + g˜ν + g˜q + 7
8 [ g˜g + g Ñ + g ˜ C ± ]=
= 2 + 3 × 2+8× 2 + 8 + 7
[3 × 4+3× 2+6× 12] +
8
+3× 4+3× 2+6× 12 + 7
[8 × 2 + 4 × 2+2× 4] =
8
= 443
4
+ 118 = 915
4
= 228.75.
(110)
The SMPP has g = 106.75 when the temperature is larger than all particle
masses (cf. equation 106) while the MSSM has g = 228.75 (which is more than
twice 106.75). In Figure 12 we sketch the curve g(T ). Notice the drastic change
on g(T ) during the QCD transition. During the EW transition the change on
the value of g(T ) is significant only when considering the MSSM.
On Table 15 we show the evolution of g(T ) for the MSSM, starting with
g(T ) = 228.75, which corresponds to the case when all particles are present
(cf. equation 110), down to g(T ) = 95.25, when the temperature equals the
threshold of the LSP. From that point on, the evolution of g(T ) proceeds within
the SMPP, according to Table 13. As already mentioned, the Higgs sector of
the MSSM contributes with eight real scalar degrees of freedom (cf. Section
1.9). Three of them get swallowed (during the EW transition) by the W ± and
Z 0 bosons. The other five are distributed by the mass eigenstates H + , H − , H 0 ,
A 0 and h 0 .