Jet fragmentation functions for $Z$-tagged jets

Understand

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 $z_h$ of the jet carried by the hadron and the transverse momentum $j_\perp$ with respect to the jet direction.
• We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_\perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions.
• We perform theoretical calculations and compare our results with the LHCb data.