Sudakov Shoulder Resummation for Thrust and Heavy Jet Mass

TL;DR

This paper investigates the origin and structure of Sudakov shoulder logarithms in thrust and heavy jet mass distributions, revealing their impact on perturbative calculations and the importance of power corrections.

Contribution

It provides a detailed analysis of Sudakov shoulder logarithms using perturbation theory and effective field theory, including the derivation of the next-to-leading logarithmic series.

Findings

Identifies the origin of Sudakov shoulder logarithms in kinematic configurations with narrow jets.

Derives the next-to-leading logarithmic series for thrust and heavy jet mass.

Highlights the significance of power corrections and Landau-pole like singularities in resummed distributions.

Abstract

When the allowed range of an observable grows order-by-order in perturbation theory, its perturbative expansion can have discontinuities (as in the $C$ parameter) or discontinuities in its derivatives (as in thrust or heavy jet mass) called Sudakov shoulders. We explore the origin of these logarithms using both perturbation theory and effective field theory. We show that for thrust and heavy jet mass, the logarithms arise from kinematic configurations with narrow jets and deduce the next-to-leading logarithmic series. The left-shoulder logarithms in heavy jet mass ($\rho$) of the form $r\ \alpha_s^n \ln^{2n}r $ with $r=\frac{1}{3}-\rho$ are particularly dangerous, because they invalidate fixed order perturbation theory in regions traditionally used to extract $\alpha_s$. Although the factorization formula shows there are no non-global logarithms, we find Landau-pole like singularities in the resummed distribution associated with the cusp anomalous dimension, and that power corrections are exceptionally important.