QCD-inspired description of multiplicity distributions in jets

TL;DR

The paper develops a universal QCD-motivated description for Polyakov-KNO multiplicity distributions $P_n(Q)$ in jets, linking the full shape and moments to the multiplicity anomalous dimension $\gamma(\alpha_s(Q))$ via the MDLA framework. By fixing minimal subleading parameters and a hadron production power for quarks, the model yields accurate descriptions of $e^+e^-$ data across full events, single-quark jets, and gluon jets, including the high-multiplicity tail and observed scaling violations. The approach demonstrates that QCD parton multiplication dynamics can quantitatively account for observed multiplicity fluctuations, while also highlighting limitations at low multiplicities and lower energies where non-perturbative effects may dominate. The results offer a coherent path to applying the framework to LHC and future collider jet data, while stressing the need for improved non-perturbative understanding and more gluon-jet measurements. All mathematical structures are expressed through $P_n(Q)$, $N(Q)$, $\nu=n/N(Q)$, ${\cal Z}(u,Q)$, $\gamma(\alpha_s)$, and related MDLA/Vocabulary terms.

Abstract

We suggest a universal QCD-motivated expression for the Polyakov-KNO multiplicity distributions of hadrons in jets and compare it with data from $e^+e^-$ annihilation experiments. The moments and overall shape of the distributions in full events and quark and gluon jets, over a range of energies, are described with reasonable quantitative precision. In particular, the scaling violation predicted by QCD is seen clearly in the moments and high-multiplicity fluctuations.

Figures (23)

• Figure 1: LEP-1 multiplicity moments
• Figure 2: LEP-1 one-hemisphere moments
• Figure 3: HRS full event and one-hemisphere multiplicity moments HRSmoms
• Figure 4: $<\!N\!>/D$ ratio
• Figure 5: Low-rank moments; numerical vs. analytic for $Q=91$ and $29\,{\rm G}{\rm e V}$