I've a question according to Antiproton production efficiency but I cannot comment/ask there before I have 50 points.. Anyhow: Why exactly is the probability so small to produce antiproton compared to produce other particles? Please not just "producing mesons is more likely or gluons and stuff" but please an precise answer. Where does the rate of 1 antiproton against about one million primary protons come from?
Particle creation crossections depend on several conditions.
Primary is available phase space in energy.
Equally imprortant quantum number conservation by strong interactions .
After that enter the coupling constants at that particular energy.
Pion creation is the easiest of all, because their mass is small and single pions can be created without violating any quantum numbers.
Kaons carry strangeness, they have to be created in pairs, . Their mass is about half of the proton mass .
Protons and neutrons carry baryon number and thus a strong interaction can only produce them in pairs conserving baryon number .
Then come the probability distributions which depend on combinatorics and coupling constants.
Pions have a quark and an antiquark so simple diagrams in first order enter the production.
Kaons have to have two quark antiquark pairs to get born, one pair conserving strangeness, and the current mass of the strange quark is ten times larger than the up or down, thus their production is much smaller than for the pions.
A proton and antiproton are made up by combining three quarks to a proton and three antiquarks to an antiproton , and these have to be generated concurrently before a proton and antiproton pair can form, which diminishes probabilities too.
This explains relative abundances.For the exact numbers one has to do the calculations , which are not simple for strong interactions. In any case the relative abundances are an observational fact from experiment that has been explained by the quark model and the QCD hypothesis.