Subleading power corrections for event shape variables in $e^+ e^-$ annihilation

We consider subleading power corrections to event shape variables in $e^+e^-$ collisions at the first order in the QCD coupling $\alpha_s$. We start from the jettiness variable $\tau_2$ and the $y_{23}$ resolution variable for the $k_T$ jet clustering algorithm and we analytically compute the corresponding cumulative cross section. We investigate the origin of the different power suppressed contributions in the two-jet limit and trace it back to their different coverage of the phase space. We extend our analysis to the case of thrust and of the $C$-parameter, and we finally discuss a class of observables that depend on a continuous parameter giving different weight to central and forward emissions and we evaluate the corresponding subleading power corrections.