Kinematic variables in deep inelastic scattering
|,||4 - momenta of the initial and final state leptons|
|,||Polar and azimuthal angle of the scattered lepton|
|4 - momentum of the initial target nucleon|
|4 - momentum of the virtual photon|
|Negative squared 4 - momentum transfer|
Quark distribution Functions
define and describe
u(x)dx ( d(x)dx ) is the average number of up (down) quarks which have a momentum fraction between x and x+dx.
Actually, the proton can contain an extra pair of quark - anti quarks. The original(u, d) quarks are called valence quarks and the extra ones sea quarks.we are allowed to separate the quark distribution function into a valence and a sea part,
The structure functions in the quark parton model can be written in terms of quark distribution functions,
The unpolarized structure function- measures the total quark number density in the nucleon, - the polarized structure function is helicity difference quark number density.
The structure functions in terms of the parton distributions can be written as,
Both models, pQCD and a hyperfine perturbed constituent quark model(CQD), show that as the scaling variable
The inclusive double polarization asymmetriesin the valence region, where the scaling variable can be written in terms of polarized and unpolarized valence quark distributions,
using the nomenclature of (6) equation, we have