Physics:Deep inelastic scattering variables

In the inclusive reaction

with l, l' leptons, N a nucleon, and H any hadronic system, the following kinematic variables are frequently used to describe the interaction (p_i is the 4-vector of particle i, and as usual File:Hepb img168.gif ):

The energy transfer or hardness:

the energy of the transferred particle, in the N rest system

the square of the mass of the hadronic system:

and the dimensionless scaling variables Bjorken x

and inelasticity

generally used is the square of the centre-of-mass energy of the l + N system

Frequently, the notation is shortened to p = p_N, k = p_l, k = pl, which gives

The corresponding Feynman diagram is the following:

is the angle between the incoming l and outgoing lepton l' directions, and m is the nucleon mass. For more details, see Abramowicz94.

Frequently, the analysis of the hadronic system is done in the Breit frame , defined to be the frame in which the momentum transfer q (usually the virtual photon) has no transverse component and the longitudinal (z) component is -Q. The plane z = 0 divides the event into the ``current hemisphere z < 0, dominated by the lepton, and the ``remnant hemisphere, opposite. For an example of analysis, Adloff97.

The same variables are used in two-photon processes, e.g. in the reaction

with one electron tagged at large angle, and the other undetected. This process is mediated by photons, one quasi-real (small four-momentum transfer k, i.e. undetected electron), the other virtual (four-momentum transfer q). The variables in this process can be viewed as deep inelastic File:Hepb img182.gif scattering; l and l' refer to the initial and final tagged electron.