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We present an updated study of transverse single-spin asymmetries for theinclusive large-$P_T$ processes $\ell \, p^\uparrow \to h\, X$ and $\ell\,p^\uparrow \to {\rm jet}\,X$, within a transverse momentum-dependent approach,including the contribution of quasireal (Weizs\"acker-Williams) photons. In thespirit of a unified transverse momentum-dependent scheme, predictions areobtained adopting the Sivers and transversity distributions and the Collinsfragmentation functions as extracted from fits to the azimuthal asymmetriesmeasured in semi-inclusive deep inelastic scattering and $e^+e^-$ annihilationprocesses. The description of the available data is extremely good, showing aclear general improvement with respect to the previous leading-order analysis.Predictions for unpolarized cross sections and single-spin asymmetries forongoing and future experiments are also given.

Transverse single-spin asymmetries in $\ell \,p^\uparrow \to h \,X$ within a TMD approach: Role of quasireal photon exchange