where I have normalized ode to typicalweak scale cross sectionsThis result suggests that for da ofthat sale and for mye in theGel TeV range decoupling happensaround

du 15 20

kosTdc MFK 0,05 mye

Let us try to get more out ofthe some equation and estimate

the contribution of these particlesto the energy density todayWe have

Sø o02 ny mai

Today

and we can relate the present number

density to the number densitywhen the DM particles decoupledthrough

t.de Mio Eda

noko nx.de IITo find adela we can use

that the entropy in a comingvolume is constant

ås constant

å g T constant

aiaas.d.la aiot s.oTo3

Only photons are relativistic todayså gets 2 We therefore have

13 II 5and so

Sno gIad mad nøgde Ifa

To til nz.de we ago back to

the criterion for decoupling

Adelaide Hd III gje k2

Ep

and one again we approximate

00 de olde kremtså

Mide É III gjklkrsTd.PLEp i

Then

hø oSKI3 22 3Hf Sko å

8 IG

Scott

I Å mai na.de Éhi E mail.EE HEI gIk

gi lkrsj.IT II IsAfter some clearing up and insertion ofnumerical constants we can writethis as

IX oh 1,697429 10 38 2

G s.de Ode

We will typically have gats taxand Gy 102 at decoupling

Taking XD 2 20 this gives

DX oh 15 1538hLOde

Så ond 10 36 un gives nyoh 0,15

which is about the right DM densitytoday Smk cross sections are

frequently fond theoretically fordark matter candidates in supersymmetric

extensions of the standard ModelSUSY was introduced in order tosolve a completely different issue

the so called hierarchy problemwhy is the mus of the Higgs bosonså mudre smaller then the Plank mars

The fact that it also at the same

time can provide a dark mattercandidate with the right propertiesis sometimes referred to as

the Susy WIMP miracle

Sadly searches for SUSY WIMPS

at the LHL and in dreit detention

dark matter experiments have so

far not given any positiveresults