# Special relativity particle creation

A photon hits a proton that is at rest (In the lab system) which creates a pion, so now there are only the proton and pion. The question is what minimal energy can you give a photon such that this reaction is possible?

I tried using conservation of energy and momentum however the $$\gamma$$ in the equations made it impossible to solve. I also tried moving to the c.m. system but because that changes the frequency and therefore the energy of the photon the algebra is again to complicated.

• You probably need to show some work. Can you draw an energy-momentum diagram (analogous to a Spacetime diagram) where the components are energy and momentum (instead of time and space). Conservation laws suggest the total-4-momentum before (vectors added tip to tail starting at the origin) equals the total after (tip to tail starting at the origin), resulting in a polygon. What does your minimal condition mean for the final total 4-momenta? (Examples of diagrams are in my answer to physics.stackexchange.com/questions/594212/… ) – robphy Jun 12 at 12:02