Sudakov Shoulder Resummation for Thrust and Heavy Jet Mass

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 (p) of the form ransln2nr with r = 31 - p are particularly dangerous, because they invalidate fixed-order perturbation theory in regions traditionally used to extract as. Although the factorization formula shows there are no nonglobal logarithms, we find Landau-pole-like singularities in the resummed distribution associated with the cusp anomalous dimension and that power corrections are exceptionally important.