Low-energy SUSY and DM 201parameters:mχ ̃ 0
1
and the temperature at whichχ ̃ 10 decouples(Tχd)which fixes
the number of survivingχ ̃ 10 s. As for the determination ofTχditself, one has to
compute theχ ̃ 10 annihilation rate and compare it with the cosmic expansion rate.
Several annihilation channels are possible with the exchange of different
SUSY or ordinary particles, ̃f, H, Z, etc. Obviously the relative importance of
the channels depends on the composition ofχ ̃ 10 :
(i) Ifχ ̃ 10 is mainly a gaugino (say at least at the 90% level) then the annihilation
goes through ̃for ̃lRexchange and the sfermion massm ̃fplays a crucial role.
The actual limits from LEP2 are roughly:mν ̃≥43 GeV and m ̃e,mq ̃≥90 GeV. (5.41)The contribution todue to neutralinosχ ̃ 0
1
is given byχ ̃ 0
1
h^20 m^2 χ ̃ 0
1+m^2 l ̃
R
(1TeV)^2 m^2 χ ̃ 0
11
(
1 −
m^2 χ ̃ 0
1
m^2 χ ̃ 0
1+m^2 ̃l
R) 2
+
m^4 χ ̃ 0
1
(m^2 χ ̃ 0
1+m^2 ̃l
R
)^2. (5.42)
If sfermions are light theχ ̃ 10 annihilation rate is fast andχ ̃ 0
1
is negligible.
However, if ̃f (and hence ̃l, in particular) is heavier than 150 GeV, the
annihilation rate ofχ ̃ 10 is sufficiently suppressed so thatχ ̃ 10 can be in the
right ball park forCDM. In fact if all the ̃fs are heavy, say above 500 GeV
and formχ ̃ 0
1
m ̃f, then the suppression of the annihilation rate can become
too efficient yieldingχ ̃ 0
1
unacceptably large.
(ii) Ifχ ̃ 10 / is mainly a combination ofH ̃ 10 andH ̃ 20 it means thatM 1 andM 2 have
to be much larger thanμ. Invoking the relation (5.38) one concludes that,
in this case, we expect heavy gluinos, typically in the TeV range. As for
the number of survivingχ ̃ 10 s in this case, what is crucial is whethermχ ̃ 0
1
is larger or smaller thanMW. Indeed, formχ ̃ 0
1
> MWthe annihilation
channelsχ ̃ 10 χ ̃ 10 →WW,ZZ,t ̄t reduceχ ̃ 0
1
too much. Ifmχ ̃ 0
1
<MWthen
acceptable contributions ofχ ̃ 10 toCDMare obtainable in rather wide areas
of the (μ−mZ) parameter space;
(iii) Finally it turns out that ifχ ̃ 10 results from a large mixing of the gaugino (W ̃ 3
andB) and higgsino ( ̃ H ̃^01 andH ̃^02 ) components, then the annihilation is too
efficient to allow the survivingχ ̃ 10 to provide a large enoughχ ̃ 0
1. Typically
in this caseχ ̃ 0
1
< 10 −^2 and henceχ ̃ 10 is not a good CDM candidate.
In the minimal SUSY standard model there are five new parameters in
addition to those already present in the non-SUSY case. Imposing the electroweak