C-Parameter Distribution at N[superscript 3]LL′ Including Power Corrections

Abstract

We compute the e[superscript +]e[superscript -] C-parameter distribution using the soft-collinear effective theory with a resummation to next-to-next-to-next-to-leading-log prime accuracy of the most singular partonic terms. This includes the known fixed-order QCD results up to O(α[3 over s]), a numerical determination of the two-loop nonlogarithmic term of the soft function, and all logarithmic terms in the jet and soft functions up to three loops. Our result holds for C in the peak, tail, and far tail regions. Additionally, we treat hadronization effects using a field theoretic nonperturbative soft function, with moments Ω[subscript n]. To eliminate an O(Λ[subscript QCD]) renormalon ambiguity in the soft function, we switch from the [bar over MS] to a short distance “Rgap” scheme to define the leading power correction parameter Ω[subscript 1]. We show how to simultaneously account for running effects in Ω[subscript 1] due to renormalon subtractions and hadron-mass effects, enabling power correction universality between C-parameter and thrust to be tested in our setup. We discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for α[subscript s](m[subscript Z]) and Ω[subscript 1], the perturbative uncertainty in our cross section is ≃ 2.5% at Q = m[subscript Z].