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Jet fragmentation functions are measured for the first time in proton-protoncollisions for charged pions, kaons, and protons within jets recoiling againsta $Z$ boson. The charged-hadron distributions are studied longitudinally andtransversely to the jet direction for jets with transverse momentum 20 $<p_{\textrm{T}} < 100$ GeV and in the pseudorapidity range $2.5 < \eta < 4$. Thedata sample was collected with the LHCb experiment at a center-of-mass energyof 13 TeV, corresponding to an integrated luminosity of 1.64 fb$^{-1}$. Tripledifferential distributions as a function of the hadron longitudinal momentumfraction, hadron transverse momentum, and jet transverse momentum are alsomeasured for the first time. This helps constrain transverse-momentum-dependentfragmentation functions. Differences in the shapes and magnitudes of themeasured distributions for the different hadron species provide insights intothe hadronization process for jets predominantly initiated by light quarks.

Multidifferential study of identified charged hadron distributions in $Z$-tagged jets in proton-proton collisions at $\sqrt{s}=$13 TeV