WIMP annihilation cross section

cohen990

Hi, I'm reading an article called SuperSymmetric Dark Matter, by G. Jungman et al. doi:10.1016/0370-1573(95)00058-5 and in section 3.2, he claims that
[itex]<σv> ≈ \alpha^{2}(100 GeV)^{-2} \approx10^{-25} cm^{3} s^{-1},[\itex] for [itex]\alpha \approx \frac{1}{100}.[/itex]

When I run through the calculation, I get 1x10[itex]^{-29}[/itex]. Have I tripped up in my calculation or am I missing an assumption somewhere?

my calculation:
[itex]\frac{0.01^{2}}{10^{4}GeV^{2}} = 1GeV^{-2}= 1GeV^{-2}(\hbar c)^{2}c = 3\times10^8\times4\times10^{-2}fm^{2}ms^{-1}=1\times10^{7}\times(\frac{1m}{10^{15}fm})^{2}ms^{-1}fm^{2} = 1\times10^{7}\times10^{-30}m^{3}s^{-1} = 1\times10^{-29}cm^{3}s^{-1}[/itex]

Also he claims that his value for Ωh[itex]^2 \approx 3\times10^{-2}[/itex] is close to the value measured [itex]\approx 0.22[/itex] but it is a full order of magnitude off...

I know that a portion of cold dark matter is in machos and in baryonic matter but that cannot account for the discrepancy between the measured value and Jungman's predicted value. Can anybody help me understand?


Thanks, Dan

mfb

I see an error in your first and last "=".

WolframAlpha gives 10^-31m^3/s, which is equivalent to 10^-31(10²cm)^3/s = 10^-25 cm^3/s.

cohen990

Ah, thanks. Silly mistake :<

Any thoughts on my second question?

mfb

Where is that claim?

One order of magnitude is not so bad for a rough estimate, concerning the magnitude of some numbers involved in particle physics and cosmology.

http://arxiv.org/abs/hepph/9506380

cohen990

Well the phrase he uses is
referring to [itex]<\sigma_{A}v>[/itex], the annihilation cross section.

mfb

The ftp links do not work :(, but this talk (pdf) has the same remark.

m can be tuned, so it is easy to find an m where Ωh² ≈ 0.1. That happens to be at the scale of EWSB, but it could be a pure coincidence.

cohen990

Thanks for your help. It makes more sense now.

Supersymmetric dark matter

If you have access, it's worth a look ^_^

Thanks again