Invariant Mass
As you have already learned, the formula for relativistic energy of a particle is

simple relativistic relationsip between energy, momentum and mass


In order to calculate the mass of the Z boson we start with the formula for the Z mass as a sum of the energies and momenta of the decay particles:

Z mass


Since we are looking at Z decays into either an electron-positron pair or a muon-antimuon pair the sum is over two particles only, giving

Z mass simple


Multiplying out the parentheses:

Z mass


You recognize the Z mass as Z mass and likewise for particle 2, (from juggling around the terms in formula (1)).

So you see that

Z mass


which, cleaned up, gives

Z mass


Taking the square root gives you the final expression of the Z mass expressed by the masses, energies and momenta of the two decay particles.



Z mass


You therefore need to know all these quantities in order to calculate the Z mass.

Here you get back to the Z measurement site.