The parton-level structure of e+e− to 2 jets at N3LO

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