Dijet mass up to four-loops with(out) ${\boldsymbol k}_{\boldsymbol t}$ clustering

Abstract

We compute the invariant mass of dijets produced in $e^+ e^-$ annihilation processes up to four loops in perturbation theory for both anti-$k_t$ and $k_t$ jet algorithms. The calculations, performed within the eikonal approximation and employing strong-energy ordering, capture the full analytic structure of the leading Abelian and non-Abelian non-global logarithms, including full colour and jet-radius dependence. We evaluate the significance of these logarithms and the convergence of the four loop perturbative expansion by comparing with all-orders numerical results.