Multiplicity distributions in QCD jets and jet topics

We evaluate the Koba-Nielsen-Olesen (KNO) scaling functions for quark- and gluon-initiated jets by incorporating energy conservation into the Double Logarithmic Approximation (DLA). The resulting modified DLA (MDLA) expressions differ substantially from the DLA predictions and qualitatively align with the recently proposed QCD-inspired expressions, albeit with some quantitative differences. By fixing the two parameters in the MDLA expressions, we show that the inclusive charged-particle multiplicity distributions of the two leading jets in $pp$ collisions at $\sqrt{s} = 13$ TeV, measured by ATLAS over a wide jet $p_T$ range of $0.1$-$2.5$ TeV, are well described within experimental uncertainties and consistent with PYTHIA simulations. This conclusion is further supported by direct comparisons with quark- and gluon-initiated jet distributions extracted via jet topics, though the propagated uncertainties from experimental data remain sizable.