Calculate Baryons Annihilation Cross Sections

[Andrea M.]

I was wondering if there is a way of calculate the annihilation cross section for two baryons, say $p\bar p\to\pi\pi$ or $p\bar p\to\gamma\gamma$. The problem here is that we cannot use the usual chiral theory because the energy transfer is of the same order of the cutoff $\Lambda\sim 1 \text{Gev}$.

In almost all the articles I have found those cross sections are derived by experimental observation, do you know possibles way to derive them theoretically?

 

[Buzz Bloom]

Hi Andrea:

I do not have any answer to your question. What I do have is a thought about why there might not be any answer. I asked a similar question about calculating the mean free path of a photon with a frequency that can be absorbed by a CO2 molecule. This calculation also involved cross section values. The discussion led to a conclusion that the answer apparently needs to be determined by experiment. Perhaps there is no related theory. Are you aware of any similar problem that does have a theoretical solution?

Regards,
Buzz

 

[Andrea M.]

Sorry for the gap, busy day. No, I don't know any solution (except for lattice QCD) for these kind of problems. The only thing that is commonly assumed in the literature is that these kind of strong process should be of order $\langle\sigma v\rangle\sim g_s/4\pi m_p$.