# Available energy of a collision and momentum calculations for proton-antiproton collisions

I am currently planning an experiment focusing on the creation of a J/psi meson through proton-antiproton collisions at a range of momenta.

The linear accelerator I have access to has a range of momenta from 0.5 GeV/c to 10 GeV/c, and I plan to collide a beam of antiprotons with stationary protons to hopefully produce a J/psi meson, which I will detect through resonance in the decay though muon-antimuon pairs.

However, I am unsure how to calculate the available energy in the collision and the necessary minimum momentum for the production of a J/psi particle. If somebody could tell me what formulae to use to calculate the available energy in a proton/antiproton collision, as well as for the calculation of the momentum I need to achieve the creation of a J/psi, I would be very appreciative.

Any suggestions regarding my experiment are also welcome.

Thank you.

• Would you be offended if I suggested you add the homework tag, bearing in mind what you are asking for? – user146020 Mar 22 '17 at 22:48
• Do you mean two J/psi's in each reaction? p+p_bar -->J/psi + J/psi +X_number of other hadrons? i.e. inclusive production of two J/psi? – anna v Mar 23 '17 at 7:24
• there exists this arxiv.org/pdf/1406.0484.pdf at much higher energies in proton proton collisions also this for pi-proton sciencedirect.com/science/article/pii/… all at much higher energies because the available phase space for production after threshold is very restricted . – anna v Mar 23 '17 at 7:35
• @annav Yes. I mean in the form of a p+p_bar = J/psi + J/psi + x event. That is unless it is possible for the production of a single J/psi particle (which I believe is prohibited by quantum field theory and quantum mechanics generally). – Franklin Mar 23 '17 at 18:21
• there is no prohibition, ccbar can be produced by gluons , and the crossection is small because of the masses. see fig 5.10 here lib.dr.iastate.edu/cgi/… Two j/psi make it even worse. All the experimental papers for hadronic production of j/psi are for 100 GeV and more, it is very improbable at 10 GeV. – anna v Mar 23 '17 at 18:39

It is good that as a high school ( from your profile) student you have an interest in particle physics, and I hope this continues to university years. I am treating your question as a thought experiment, and will comment accordingly:

focusing on J/psi pair production through proton-antiproton collisions at a range of momenta.

The J/psi meson has a mass of 3.1 GeV ( in a system where c=1).

By j/psi pair production you must mean : by looking for e+e- pairs produced in the antiproton proton scattering.

The decay modes of the J/psi are mostly to hadrons, but there is a substantial fraction that goes to e+e- and mu+mu- ( ~12%).

to collide a beam of antiprotons with protons in a bound state

There does exist a bound state of proton antiproton, called protonium, but when colliding a proton and an antiproton at high energies they do not bind because their respective energies are too high. Protonium may exist as a resonance in the decay products, but this is not what you are describing. You want a proton antiproton collision to give, among the products of the collision, lepton antilepton pairs whose invariant mass may show the J/Psi resonance.

The linear accelerator I have access to has a range of momenta from 0.5 GeV/c to 10 GeV/c,

To find the energy available for particle generation after the collision, one has to find the input energy. The input energy of each, proton and antiproton is given by adding their four vectors , an example can be found here .

The incoming energy must be higher than the mass of the J/psi as energy, so there is a threshold energy incoming for seeing J/psi production. An experiment needs high energies to have a probability of generating such a heavy resonance as the J/psi. My impression is that only at the tevatron energies this experiment could be realized.