Matching Collinear and Transverse Momentum Dependent Observables in the CSS Formalism

We report on the improved Collins-Soper-Sterman (iCSS) formalism presented in, in particular for the case of polarized observables, such as the Sivers effect in semi-inclusive deep-inelastic scattering. We also outline how this study can be extended beyond leading order to address the matching of collinear PDFs to transverse momentum integrated TMDs.