1. The problem statement, all variables and given/known data An accelerator experiment collides a beam of electrons head-on with a beam of positrons. The particles in each beam have energy Ee as measured in the lab frame. Suppose one electron-positron pair collide to form a photon and neutral pion particle: e- = e+ ---> γ + π0 Assuming 2Ee > mπ, where mπ is the mass of the pion show that the sped vπ of the pion in the lab frame is given by vπ = 4Ee2 - mπ2 / 4Ee2 + mπ2 2. Relevant equations The invariant: E2 - p2c2 = m2c4 Conservation of energy Conservation of momentum 3. The attempt at a solution The first place I've been getting confused is that the electron and positron have the same momenta but in opposite directions. Not entirely sure if I should be including their momentum in the equations as it sums to zero. In a collision their momentum towards each other would surely contribute to the rest energy, kinetic energy and photon energy of the collision products. I've been attempting to use conservation of energy: 2Ee = 2√(me2 + pe2) = √(mπ2 + pπ2) + cpγ Then conservation of momentum: pe- + pe+ = pπ + pγ We know that the electron have opposite momentum so their sum equals zero and .. pπ = - pγ So this gets rid of any photon terms from the equation, 2Ee = 2√(me2 + pe2) = √(mπ2 + pπ2) + cpπ Now, I figured I should solve this for pπ, use that to find the pion energy and then it's velocity but it doesn't solve nicely and doesn't look anything like the equation given in the question. Been working on this for a while but I'm not coming up with anything.