·        is the usual three momentum

·       E is the energy

is an invariant.

Let us evaluate this in a general frame

•  is  three vector dot product.

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

reactions:

•   inclusive

•    exclusive  elastic

•     delta production 1st  proton resonant excitation

•  1st inelastic channel

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:

•    absorption of a virtual photon.

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