  In view of the increasing precision of theoretical calculations and
experimental measurements, power corrections to transverse-momentum-dependent
observables are highly important. We study the next-to-leading power
corrections for transverse momentum measurements in $e^+ e^- \rightarrow 2$
jets. We obtain a factorized expression for the cross section, which involve
twist-2 and twist-3 operators, and identify the new jet functions that appear
in it. We calculate these jet functions at order {\alpha}s for a family of
recoil-free schemes, and provide the corresponding anomalous dimensions at
leading order. Additionally, we show that the (endpoint) divergences that
typically arise in sub-leading-power factorization can be subtracted and cancel
for our case. By working with jets, everything is perturbatively calculable and
there are substantial simplifications compared to the general next-to-leading
power framework. Importantly, our analysis with jets can be extended to
semi-inclusive deep-inelastic scattering, with the future Electron-Ion Collider
as key application.
