_{}
· _{} 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 _{}
_{}
reactions:
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 è 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
_{}