Parton Distributions

The parton distribution function $f_i^a(x,Q^2)$ parameterizes the probability to find a parton $i$ with a fraction $x$ of the beam energy when the beam particle $a$ is probed by a hard scattering at virtuality scale $Q^2$. Usually the momentum-weighted combination $x f_i^a(x,Q^2)$ is used, for which the normalization condition $\sum_i \int_0^1 dx \, x f_i^a(x,Q^2) \equiv 1$ normally applies. The $Q^2$ dependence of parton distributions is perturbatively calculable, see section .

The parton distributions in PYTHIA come in many shapes, as shown in the following.