Oriented Event Shapes at N3LL + O(as^2)

Abstract

We analyze oriented event-shapes in the context of Soft-Collinear Effective Theory (SCET) and in Fixed-Order perturbation theory. Oriented event-shapes are distributions of event-shape variables which are differential on the angle theta_T that the thrust axis forms with the electron-positron beam. We show that at any order in perturbation theory and for any event shape, only two angular structures can appear: F_0 = 3/8(1 + cos^2 theta_T) and F_1 = (1 - 3cos^2 theta_T). When integrating over theta_T to recover the more familiar event-shape distributions, only F_0 survives. The validity of our proof goes beyond perturbation theory, and hence only these two structures are present at the hadron level. The proof also carries over massive particles. Using SCET techniques we show that singular terms can only arise in the F_0 term. Since only the hard function is sensitive to the orientation of the thrust axis, this statement applies also for recoil-sensitive variables such as Jet Broadening. We carry out resummation at N3LL of singular terms for Thrust, Heavy-Jet Mass, the sum of the Hemisphere Masses and C-parameter. We also compute the Fixed-Order distributions for these event-shapes at O(as) analytically and at O(as^2) with the program Event2.

29 pages, 10 figures. Extended discussion on SCET proof. Added a plot comparing to experimental data. References added. Conclusions unchanged. Matches published version

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Cited by in corpus (10)

• 50 Years of Quantum Chromodynamics
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• A Precise Determination of ${\alpha }_s$ from the C-parameter Distribution
• Massive Event-Shape Distributions at N${}^2$LL
• NLO Massive Event-Shape Differential and Cumulative Distributions
• Logarithmically-accurate and positive-definite NLO shower matching
• Precision $e^{+}{e}^{-}$ Hemisphere Masses in the Dijet Region with Power Corrections
• Subleading power corrections for event shape variables in $e^{+}{e}^{-}$ annihilation
• NLO Oriented Event-Shape Distributions for Massive Quarks
• Oriented Event Shapes for massive Quarks