Abstract
We investigate the quantum chromodynamics (QCD) corrections to hadronic final states in electron-positron collisions at mathcal{O} ( {alpha}_s^3 ) in the strong coupling constant αs. Namely, we analytically compute the total cross section for this process by separately integrating the tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements over the respective phase space. All the contributions to the calculation are treated in a common framework whereby phase space integrals are expressed as physical cuts of the four-loop two-point function. We check the cancellation of infrared poles at all colour levels and we reproduce the known result for the R-ratio at order {alpha}_s^3 .
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