s

^{2}=(E

_{1}+E

_{2})

^{2}-c

^{2}(p

_{1}+p

_{2})

^{2}=constant

to a simple homework problem in modern physics, and I'm not exactly sure how. There've been several problems so far that have applied this, but generally I've been able to work in the center-of-mass frame and rule out momenta.

However, this problem: "What is the minimum energy that a gamma ray must have in order to produce the reaction p+gamma--->p+pi

^{0}, when p (a proton) is at rest. Note that m

_{p}c

^{2}=940MeV and m

_{pi}c

^{2}=140MeV."

Requires that I not use that approach. So what I've got down on my paper is

s

^{2}=(m

_{p}c

^{2})

^{2}-c

^{2}(p

_{gamma})

^{}=(E

_{p}+E

_{pi})

^{2}-c

^{2}(....)

^{2}

So cp

_{gamma}is what I'm solving for, but I have no idea what to put in the parentheses on the right-hand-side with the ellipses. I've got the solution for p

_{gamma}c: 150MeV, and using that to solve backwards for the sum of the momenta of p and pi

^{0}, I'm coming up with numbers that I can't seem to reason out of the given information by another method.

I've read and re-read the relevant sections of the text, but I'm not getting ahead.