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

TL;DR

This paper investigates oriented event-shapes in electron-positron collisions using SCET and fixed-order calculations, revealing only two angular structures at all perturbative orders and performing high-precision resummation and fixed-order computations.

Contribution

It proves that only two angular structures appear in oriented event-shapes at all orders and extends this result beyond perturbation theory, including massive particles.

Findings

Only two angular structures, F_0 and F_1, appear in all orders.

Singular terms arise only in the F_0 component.

Resummation at N3LL achieved for key event-shapes.

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.