Joint ECFA-NuPECC-APPEC Workshop “Synergies between the EIC and the LHC”

We present a phenomenological analysis for hadron-in-jet production in (un)polarized $pp$ collisions within a TMD approach, based on recent extractions of TMD fragmentation functions (TMD FFs) from SIDIS and $e^+e^-$ processes. The general agreement of our estimates with the available data corroborates the hypothesis of the TMD factorization for such processes as well as of the universality of TMD FFs. Open issues and future improvements, on both the experimental and the theoretical side, are also discussed.