$C$ parameter distribution at ${\mathrm{N}}^{3}{\mathrm{LL}}^{\text{'}}$ including power corrections
We compute the e ^{+} e ^{} C parameter distribution using the softcollinear effective theory with a resummation to nexttonexttonexttoleadinglog prime accuracy of the most singular partonic terms. This includes the known fixedorder QCD results up to O (α$$3\atop{s}$$) , a numerical determination of the twoloop 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 _{n}. To eliminate an O (Λ _{QCD}) renormalon ambiguity in the soft function, we switch from the $$\overline{MS}$$ to a short distance “Rgap” scheme to define the leading power correction parameter Ω _{1}. We show how to simultaneously account for running effects in Ω _{1} due to renormalon subtractions and hadronmass effects, enabling power correction universality between C parameter and thrust to be tested in our setup. Finally, we discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for α _{s}(m _{Z}) and Ω _{1}, the perturbative uncertainty in our cross section is ≃ 2.5 % at Q = m _{Z}.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[2]}
 Univ. of Vienna (Austria). Erwin Schrödinger International Inst. for Mathematical Physics, Faculty of Physics
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
 Univ. of Vienna (Austria). Faculty of Physics
 Publication Date:
 Grant/Contract Number:
 SC0011090
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 91; Journal Issue: 9; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society (APS)
 Research Org:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1505750
 Alternate Identifier(s):
 OSTI ID: 1179762
Hoang, André H., Kolodrubetz, Daniel W., Mateu, Vicent, and Stewart, Iain W.. C parameter distribution at N3LL' including power corrections. United States: N. p.,
Web. doi:10.1103/physrevd.91.094017.
Hoang, André H., Kolodrubetz, Daniel W., Mateu, Vicent, & Stewart, Iain W.. C parameter distribution at N3LL' including power corrections. United States. doi:10.1103/physrevd.91.094017.
Hoang, André H., Kolodrubetz, Daniel W., Mateu, Vicent, and Stewart, Iain W.. 2015.
"C parameter distribution at N3LL' including power corrections". United States.
doi:10.1103/physrevd.91.094017. https://www.osti.gov/servlets/purl/1505750.
@article{osti_1505750,
title = {C parameter distribution at N3LL' including power corrections},
author = {Hoang, André H. and Kolodrubetz, Daniel W. and Mateu, Vicent and Stewart, Iain W.},
abstractNote = {We compute the e + e C parameter distribution using the softcollinear effective theory with a resummation to nexttonexttonexttoleadinglog prime accuracy of the most singular partonic terms. This includes the known fixedorder QCD results up to O (α$3\atop{s}$) , a numerical determination of the twoloop 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 Ωn. To eliminate an O (Λ QCD) renormalon ambiguity in the soft function, we switch from the $\overline{MS}$ to a short distance “Rgap” scheme to define the leading power correction parameter Ω1. We show how to simultaneously account for running effects in Ω1 due to renormalon subtractions and hadronmass effects, enabling power correction universality between C parameter and thrust to be tested in our setup. Finally, we discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for αs(mZ) and Ω1, the perturbative uncertainty in our cross section is ≃ 2.5 % at Q = mZ.},
doi = {10.1103/physrevd.91.094017},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 9,
volume = 91,
place = {United States},
year = {2015},
month = {5}
}