Emergence of KNO scaling in multiplicity distributions in jets produced at the LHC

In this work we study the multiplicity distributions (MDs) of charged particles within jets in proton-proton collisions, which were measured by the ATLAS collaboration in 2011, 2016 and 2019. The first data set refers to jets with lower transverse momenta ($4<p_T<40$ GeV ) whereas the other two refer to higher $p_T$ jets ($0.1<p_T<2.5$ TeV). We find that the first set shows no sign of KNO scaling whereas the higher $p_T$ sets gradually approach the scaling limit. In the first set the mean multiplicity as a function of $p_T$ can be well described by expressions derived from QCD with different approximation schemes. For higher ($>500$ GeV) values of $p_T$ these expressions significantly overshoot the data. We show that the behavior of the MDs can be well represented by a Sub-Poisson distribution with energy dependent parameters. In the range $40<p_T<100$ GeV there is a transition from sub to super poissonian behavior and the MD evolves to a geometric distribution, which shows KNO scaling. In this way we fit the MDs in all transverse momentum intervals with one single expression. We discuss the implications of this phenomenological finding.