NNLO corrections to 2-jet observables in electron-positron annihilation

TL;DR

The paper develops a general-purpose NNLO subtraction framework based on antenna functions to compute infrared-safe $2$-jet observables in $e^+e^-$ annihilation. It details the required two-loop, one-loop, and Born amplitudes, the antenna subtraction terms, and the phase-space generation strategy with azimuthal averaging to ensure local cancellation of singularities. Numerical results for the Durham $2$-jet observable yield $B^{(2-jet)}=-13.674(4)$ and $C^{(2-jet)}=-231.6(0.3)$, with cross-checks showing $B^{(tot)}=2.005(6)$ and $C^{(tot)}=6.0(0.5)$, validating the approach against known inclusive cross sections. The work demonstrates the feasibility of process-wide NNLO predictions for jet observables and provides a blueprint for extending to $e^+e^- o 3$ jets or hadronic collisions.

Abstract

I report on a numerical program, which can be used to calculate any infra-red safe two-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The calculation is based on the subtraction method. The result for the two-jet cross section is compared to the literature.