Baryons annihilation

Question

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? Or can you suggest me an article or review about that?

Answer 1

This is non-perturbative QCD, so at low energy you cannot do much more than phenomenology or use experimental data. Both of the processes are somewhat rare. There is a lot of energy available, and the mean number of produced pions is 5 or 6, even at threshold (data like this can be found in the Particle Data Group tables).

At high energy these processes are exclusive reactions that can be studied using perturbative QCD. This is easier for $\bar{p}p\to\gamma\gamma$, which can be expressed (I think) in terms of a single non-perturbative parameter (so the energy dependence is predicted, and the parameter can be related to other processes), see http://journals.aps.org/prd/abstract/10.1103/PhysRevD.24.1808. Work that extends this formalism to somewhat lower energies can be found in http://arxiv.org/abs/hep-ph/0206288.