Subleading power corrections for N-jettiness subtractions

Abstract

The N-jettiness observable T[subscript N] provides a way of describing the leading singular behavior of the N-jet cross section in the τ=T[subscript N]/Q→0 limit, where Q is a hard interaction scale. We consider subleading-power corrections in the τ≪1 expansion, and employ soft-collinear effective theory to obtain analytic results for the dominant α[subscript s]τlnτ and α[superscript 2][subscript s]τln[superscript 3]τ subleading terms for thrust in e[superscript +]e[superscript -] collisions and 0-jettiness for q[bar over q]-initiated Drell-Yan–like processes at hadron colliders. These results can be used to significantly improve the numerical accuracy and stability of the N-jettiness subtraction technique for performing fixed-order calculations at next-to-leading order and next-to-next-to-leading order. They reduce the size of missing power corrections in the subtractions by an order of magnitude. We also point out that the precise definition of N-jettiness has an important impact on the size of the power corrections and thus the numerical accuracy of the subtractions. The sometimes employed definition of N-jettiness in the hadronic center-of-mass frame suffers from power corrections that grow exponentially with rapidity, causing the power expansion to deteriorate away from central rapidity. This degradation does not occur for the original N-jettiness definition, which explicitly accounts for the boost of the Born process relative to the frame of the hadronic collision, and has a well-behaved power expansion throughout the entire phase space. Integrated over rapidity, using this N-jettiness definition in the subtractions yields another order of magnitude improvement compared to employing the hadronic-frame definition.