Primordial Black Holes and Cosmological Phase Transitions Report ...
Primordial Black Holes and Cosmological Phase Transitions Report ... 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 .
PBHs and Cosmological Phase Transitions 57 Table 15: The evolution of the number of degrees of freedom g(T ) in the Universe according to the MSSM (SPS1a scenario, see Section 1.9) starting with g(T ) = 228.75, which corresponds to the case when all particles are present. As the expansion goes on, and the temperature T decreases, some particle species cease to exist (because T eventually gets below the particle threshold) lowering the value of g(T ). At the bottom we have the case g(T ) = 95.25 which corresponds to the threshold of the LSP. From that point on, the evolution of g(T ) proceeds within the SMPP (Table 13). Temperature (GeV) Particles gi g(T ) > 607.1 228.75 607.1 ˜g 16 7 214.75 585.5 570.1 ˜t2 ˜cL 8 6 208.75 ˜ dL 12 196.75 564.7 ũL ˜sL 12 184.75 547.2 546.9 ũL ˜sL ˜cR 12 172.75 ˜ 545.7 506.3 432.7 dR ˜b2 ˜b1 H 12 6 6 160.75 154.75 148.75 ± 2 146.75 425.0 H0 1 145.75 424.9 A0 1 144.75 415.4 C ˜± 2 4 7 413.9 Ñ4 8 2 141.25 7 400.5 Ñ3 8 2 139.50 7 366.5 ˜t1 8 6 137.75 131.75 194.9 ˜τL 2 129.75 189.9 183.9 ˜eL ˜µL Ñ2 4 2 125.75 7 8 124.00 120.50 183.7 ˜ C ± 1 4 7 8 172.5 t 12 7 8 110.00 172.5 ˜νe ˜νµ 4 106.00 170.5 ˜ντ 2 104.00 125.3 ˜eR ˜µR 4 100.00 107.9 ˜τR 2 98.00 116.0 h0 1 97.00 95.25 97.7 Ñ1 2 7 8
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PBHs <strong>and</strong> <strong>Cosmological</strong> <strong>Phase</strong> <strong>Transitions</strong> 57<br />
Table 15: The evolution of the number of degrees of freedom g(T ) in the Universe<br />
according to the MSSM (SPS1a scenario, see Section 1.9) starting with<br />
g(T ) = 228.75, which corresponds to the case when all particles are present. As<br />
the expansion goes on, <strong>and</strong> the temperature T decreases, some particle species<br />
cease to exist (because T eventually gets below the particle threshold) lowering<br />
the value of g(T ). At the bottom we have the case g(T ) = 95.25 which corresponds<br />
to the threshold of the LSP. From that point on, the evolution of g(T )<br />
proceeds within the SMPP (Table 13).<br />
Temperature (GeV) Particles gi g(T )<br />
> 607.1 228.75<br />
607.1 ˜g 16 7 214.75<br />
585.5<br />
570.1<br />
˜t2<br />
˜cL<br />
8<br />
6 208.75<br />
˜ dL 12 196.75<br />
564.7 ũL ˜sL 12 184.75<br />
547.2<br />
546.9<br />
ũL ˜sL<br />
˜cR<br />
12 172.75<br />
˜ 545.7<br />
506.3<br />
432.7<br />
dR<br />
˜b2 ˜b1 H<br />
12<br />
6<br />
6<br />
160.75<br />
154.75<br />
148.75<br />
± 2 146.75<br />
425.0 H0 1 145.75<br />
424.9 A0 1 144.75<br />
415.4 C ˜± 2 4 7<br />
413.9 Ñ4<br />
8<br />
2<br />
141.25<br />
7<br />
400.5 Ñ3<br />
8<br />
2<br />
139.50<br />
7<br />
366.5 ˜t1<br />
8<br />
6<br />
137.75<br />
131.75<br />
194.9 ˜τL 2 129.75<br />
189.9<br />
183.9<br />
˜eL ˜µL<br />
Ñ2<br />
4<br />
2<br />
125.75<br />
7<br />
8 124.00<br />
120.50<br />
183.7 ˜ C ± 1 4 7<br />
8<br />
172.5 t 12 7<br />
8<br />
110.00<br />
172.5 ˜νe ˜νµ 4 106.00<br />
170.5 ˜ντ 2 104.00<br />
125.3 ˜eR ˜µR 4 100.00<br />
107.9 ˜τR 2 98.00<br />
116.0 h0 1 97.00<br />
95.25<br />
97.7 Ñ1 2 7<br />
8
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