First Subleading Power Resummation for Event Shapes

Understand

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables $\tau$ at subleading power in the $\tau\ll 1$ expansion.

• These equations involve a class of universal jet and soft functions arising through operator mixing, which we call $\theta$-jet and $\theta$-soft functions.
• An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in $\alpha_s$, and provide field theory definitions of all ingredients.
• As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for $H\to gg$ in pure glue QCD.