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 $\alpha \approx \frac{1}{100}.$<br /> <br /> When I run through the calculation, I get 1x10$^{-29}$. Have I tripped up in my calculation or am I missing an assumption somewhere?<br /> <br /> my calculation:<br /> $\frac{0.01^{2}}{10^{4}GeV^{2}} = 1GeV^{-2}= 1GeV^{-2}(\hbar c)^{2}c = 3\times10^8\times4\times10^{-2}fm^{2}ms^{-1}=1\times10^{7}\times(\frac{1m}{10^{15}fm})^{2}ms^{-1}fm^{2} = 1\times10^{7}\times10^{-30}m^{3}s^{-1} = 1\times10^{-29}cm^{3}s^{-1}$<br /> <br /> Also he claims that his value for Ωh$^2 \approx 3\times10^{-2}$ is close to the value measured $\approx 0.22$ but it is a full order of magnitude off...<br /> <br /> 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?<br /> <br /> <br /> Thanks, Dan[/itex]

 

[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?

Also he claims that his value for Ωh2≈3×10−2 is close to the value measured ≈0.22 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?

 

[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[/size]

 

[cohen990]

Well the phrase he uses is

This is remarkably close to the value required to account for the dark matter in the Universe, especially if we realize that there is no a priori reason for a weak-scale interaction to have anything to do with closure density, a cosmological parameter!

referring to $<\sigma_{A}v>$, the annihilation cross section.

 

[mfb]

The ftp links do not work :(, but http://theory.fnal.gov/jetp/talks/feng.pdf (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