# Colliding beams vs static target

In this problem I need to find the threshold energy of a positron-electron collision that creates a Z boson (the reverse of the following picture; Z mass 92 GeV) in two distinct cases: collision ring and static target. For the collision ring, where proton and electron have equal but opposite momentum, I found a kinetic energy of approximately 46 GeV for each particle. However, in the static target case, where the electron is at rest, I found a beam energy of $8.6\times 10^{6}$ GeV.

This seems way too high, but I checked my calculations a couple times and I don't see any mistake. Is this a reasonable value?

• This problem (and ones similar to it) is given a lot for a reason. I haven't (and won't) check you figures, but this effect occurs in non-relativistic regimes to a degree as well and you may be applying intuition that is based on a Newtonian understanding. Think about what the velocity addition law does for you in this case; or about the difference in speed between the beam and the CoM in the fixed target version of the experiment. May 5 '16 at 0:57
• Wouldn't you usually say that $\sqrt{s}$ = 92 GeV? Then for a fixed target experiment we know that $\sqrt{s}=E_{\text{CM}}\approx\sqrt{E_{\text{proton}}}$. From that, we would conclude that $E_{\text{proton}}=s=8464$GeV. That would be 8.4 TeV which is realistic for such a configuration, but not realizable with current technology i think. May 18 '16 at 20:51