is the usual three momentum

       E is the energy


is an invariant.


Let us evaluate this in a general frame



and we identify the energy for a particle at rest as the mass energy






Consider energy and momentum conservation in lab frame. There is a symmetry for rotations about the z-axis. This means that we can choose a scattering plane and the kinematics will be the same as we rotate this plane around z-axis.


It is customary to define the scattering angle .

Notice that the diagrams above all show an exchange of a virtual photon. The photon is virtual because it is an internal line of a Feynman diagram. The reaction is in a sense simplified by considering the reaction as:


The photon can be characterized by its 3-momentum and its energy or mass.

There are several kinematical variables used to describe electron scattering:


photon mass scale since the distance of propagation depends on this mass the interaction scale it is used to characterize the size that is probed

energy transfer to the proton

momentum transfer to the proton

final momentum of X

final energy of X

invariant mass of the final state



Suppose you identify the three particle in the final state so that you know their rest masses.


For two particles