C-parameter distribution at N3LL′ including power corrections

We compute the e(+)e(-) 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(alpha(3)(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 Omega(n). To eliminate an O(Lambda(QCD)) renormalon ambiguity in the soft function, we switch from the (MS) over bar to a short distance Rgap scheme to define the leading power correction parameter Omega(1). We show how to simultaneously account for running effects in Omega(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 alpha(s)(m(Z)) and Omega(1), the perturbative uncertainty in our cross section is similar or equal to 2.5% at Q = m(Z).