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The heavy jet mass event shape has large perturbative logarithms near theleading order kinematic threshold at $\rho = \frac{1}{3}$. Catani and Webbernamed these logarithms Sudakov shoulders and resummed them atdouble-logarithmic level. A resummation to next-to-leading logarithmic levelwas achieved recently. Here, we extend the resummation using an effective fieldtheory framework to next-to-next-to-leading logarithmic order and show how tocombine it with the resummation of dijet logarithms. We also solve the openproblem of an unphysical singularity in the resummed momentum spacedistribution, in a way similar to how it is resolved in the Drell-Yan $q_T$spectrum: through a careful analysis of the kinematics and scale-setting inposition space. The heavy jet mass Sudakov shoulder is the first observablethat does not involve transverse momentum for which position space resummationis critical. These advances may lead to a more precise extraction of the strongcoupling constant from $e^+ e^-$ data.

NNLL Resummation of Sudakov Shoulder Logarithms in the Heavy Jet Mass Distribution