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We analyze oriented event-shapes in the context of Soft-Collinear EffectiveTheory (SCET) and in Fixed-Order perturbation theory. Oriented event-shapes aredistributions of event-shape variables which are differential on the angletheta_T that the thrust axis forms with the electron-positron beam. We showthat at any order in perturbation theory and for any event shape, only twoangular 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 familiarevent-shape distributions, only F_0 survives. The validity of our proof goesbeyond perturbation theory, and hence only these two structures are present atthe hadron level. The proof also carries over massive particles. Using SCETtechniques we show that singular terms can only arise in the F_0 term. Sinceonly the hard function is sensitive to the orientation of the thrust axis, thisstatement 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 theFixed-Order distributions for these event-shapes at O(as) analytically and atO(as^2) with the program Event2.

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