Jet fragmentation functions for Z-tagged jets

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside Z-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction zh of the jet carried by the hadron and the transverse momentum j⊥ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the zh-dependence provides information on standard collinear fragmentation functions, while j⊥-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate zh region. For j⊥-dependence, we suggest binning in both zh and j⊥, which would lead to a more direct probing of TMD fragmentation functions.