C-parameter distribution at N super(3)LL' including power corrections

• Published in: Physical review. D, Particles, fields, gravitation, and cosmology Vol. 91; no. 9
• Main Authors: Hoang, Andre H, Kolodrubetz, Daniel W, Mateu, Vicent, Stewart, Iain W
• Format: Journal Article
• Language: English
• Published: 01-05-2015
• Subjects: Ambiguity; Asymptotic properties; Constants; Gravitation; Mathematical analysis; Mathematical models; Subtraction; Texts
• ISSN: 1550-7998; 1550-2368

The authors compute event shapes, focusing in particular on the C-parameter distribution, in electron-positron collisions at next-to-next-to-next-to leading order using Soft Collinear Effective Theory. Such higher loop calculations of event shape variables are essential to continuing progress in determining the strong coupling constant. We compute the e super(+)e super(-) 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 (ProQuest: Formulae and/or non-USASCII text omitted), 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] sub(n). To eliminate an O( Delta sub(QCD)) renormalon ambiguity in the soft function, we switch from the MS to a short distance "Rgap" scheme to define the leading power correction parameter [Omega] sub(1). We show how to simultaneously account for running effects in [Omega] sub(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 sub(s)(m sub(Z)) and [Omega] sub(1), the perturbative uncertainty in our cross section is [Asymptotically = to] 2.5% at Q = m sub(Z).