# Perturbative QCD

Perturbative QCD is a subfield of particle physics in which the theory of strong interactions, Quantum Chromodynamics (QCD), is studied by using the fact that the strong coupling constant ${\displaystyle \alpha _{s}}$ is small in high energy or short distance interactions, thus allowing perturbation theory techniques to be applied. In most circumstances, making testable predictions with QCD is extremely difficult, due to the infinite number of possible topologically-inequivalent interactions. Over short distances, the coupling is small enough that this infinite number of terms can be approximated accurately by a finite number of terms. Although limited in scope, this approach has resulted in the most precise tests of QCD to date[citation needed].
An important test of perturbative QCD is the measurement of the ratio of production rates for ${\displaystyle e^{+}e^{-}\to {\text{hadrons}}}$ and ${\displaystyle e^{+}e^{-}\to \mu ^{+}\mu ^{-}}$. Since only the total production rate is considered, the summation over all final-state hadrons cancels the dependence on specific hadron type, and this ratio can be calculated in perturbative QCD.