The variables on which the parton distributions depend
Parton distribution functions give the number of partons (quarks and
gluons) in a high momentum proton or other hadron. Precisely, the
parton distribution
gives the distribution of partons of type a in a hadron
of type A.
Flavors
Here a could be
- any flavor of antiquark
- anti-up
- anti-down
- anti-strange
- anti-charm
- anti-bottom
- anti-top
- any flavor of quark
- up
- down
- strange
- charm
- bottom
- top
- gluon
The label A can designate proton, anti-proton, neutron, pion, ....
In these pages we treat only A = proton. The anti-proton case
is obtained by exchanging quarks with antiquarks. The neutron case is obtained
by interchanging up with down quarks and interchanging anti-up with anti-down
antiquarks. We do not discuss pions and other hadrons here.
Momentum fraction
The function f gives parton distribution as a function of the
fraction x of the proton's momentum that is carried by the parton. Precisely,
f dx represents the number of partons with momentum fraction
between x and x + dx.
Scale dependence
The parton distribution functions depend on a scale mu. Mathematically, this
scale specifies the momentum scale of the renormalization of the operators
that appear in the definition. Physically, when parton distribution functions
are used to make QCD predictions for a physical process, mu is set to be
of the same approximate size as the momenta involved in the process.
The parton distribution functions vary as mu is changed according to an
evolution equation usually known as the Gribov-Lipatov-Altarelli-Parisi
(GLAP) equation.
Davison E. Soper and Parvez Anandam
Institute of Theoretical Science,
University of Oregon, Eugene OR 97403 USA
soper@bovine.uoregon.edu
anandam@darkwing.uoregon.edu