Modified Weibull and Tsallis Distributions for multiplicities in $e^{+}e^{-}$ collisions at LEP2 energies

TL;DR

This study compares charged particle multiplicity distributions in $e^{+}e^{-}$ collisions at LEP2 energies with Tsallis $q$-statistics and Weibull distributions, finding Tsallis explains the data well while Weibull does not, even after modifications.

Contribution

The paper introduces modified Weibull and Tsallis distributions to better fit multiplicity data from LEP2, highlighting the effectiveness of Tsallis over Weibull.

Findings

Tsallis $q$-statistics fits the data well across all energies.

Original Weibull distribution fails to capture data properties.

Modified Weibull improves data description but remains less effective than Tsallis.

Abstract

Multiplicity distributions of charged particles produced in the $e^{+}e^{-}$ collisions at LEP2 energies ranging from 91 to 206 GeV in full phase space, are compared with predictions from Tsallis $q$-statistics and the recently proposed Weibull distribution functions.~The analysis uses data from two LEP experiments, L3 and OPAL.~It is shown that Tsallis $q$-statistics explains the data in a statistically acceptable manner in full phase space at all energies, while the Weibull distribution fails to explain the underlying properties of the data.~Modifications to the distributions proposed earlier, are applied to uncover manifold improvements in explaining the data characteristics.