Non-universal Milan factors for QCD jets

Using the dispersive method we perform a two-loop analysis of the leading non-perturbative power correction to the change in jet transverse momentum $p_T$, in the small $R$ limit of a Cambridge-Aachen jet clustering algorithm. We frame the calculation in such a way so as to maintain connection with the universal "Milan factor" that corrects for the naive inclusive treatment of the leading hadronization corrections. We derive an enhancement factor that differs from the universal Milan factor computed for event-shape variables as well as the corresponding enhancement factor previously derived for the $k_t$ algorithm. Our calculation directly exploits the soft and triple-collinear limit of the QCD matrix element and phase space, which is relevant for capturing the coefficient of the leading $1/R$ power correction. As an additional check on our new calculational framework, we also independently confirm the known result for the $k_t$ algorithm.