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

Abstract We compute the invariant mass of dijets produced in $$e^+ e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> annihilation processes up to four loops in perturbation theory for both anti- $$k_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> and $$k_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> 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.