Exploring soft anomalous dimensions for $1/Q$ power corrections

In this article we study, via analytical methods, $1/Q$ non-perturbative power corrections to event shape mean values, addressing in particular the question of their interplay with soft perturbative emissions. Specifically we point out that energy-ordered soft perturbative emissions that precede a non-perturbative emission, give rise to terms of the form $\frac{1}{Q} \left (\alpha_s \ln \frac{Q}{\Lambda} \right)^n$. While such terms are formally higher order in the strong coupling, their form suggests that they can numerically compete with the leading $1/Q$ term while also modifying the $Q$ dependence of the result. The resummation of such power-suppressed but logarithmically enhanced terms lends an anomalous dimension to the leading $1/Q$ power correction. In order to argue for the presence of such an anomalous dimension, we formulate a method to compute the first order in $\alpha_s$ correction for the mean values of the thrust $1-T$ and $C$-parameter observables. We comment on our findings in light of the standard picture of universality of $1/Q$ power corrections for event shape variables and implications for phenomenology.