Parton Distribution Functions

Quarks and gluons inside the proton — Bjorken scaling and DGLAP evolution

Q² scale (GeV²) 31.6 GeV²
Bjorken x probe x = 0.100
Probe beam energy 100 GeV
0.100
Bjorken x
0.42
u(x) valence
1.85
g(x) gluon
0.65
Gluon mom. fraction

About

Parton distribution functions (PDFs) f(x, Q²) give the probability of finding a parton (quark or gluon) carrying momentum fraction x of the proton at resolution scale Q². They cannot be calculated from first principles (nonperturbative QCD) but evolve with Q² via the DGLAP equations. At low x, gluon density rises steeply as xg(x,Q²) ~ x^{−0.3}. At Bjorken scaling, F₂(x) depends only on x — evidence for pointlike constituents inside the proton, discovered at SLAC in 1968.