Non-extensivity of the QCD pT spectra

TL;DR

This paper explores the connection between high-momentum hadronic distributions in proton-proton collisions and Tsallis non-extensive statistics, aiming to unify perturbative QCD predictions with empirical spectral data.

Contribution

It establishes a link between QCD-based perturbative predictions and Tsallis statistics, deriving a specific non-extensivity parameter value from high-momentum spectra.

Findings

Derived q=1.25 from matching QCD and Tsallis statistics.

Showed Tsallis statistics effectively describes experimental spectra.

Connected asymptotic QCD behavior with non-extensive thermodynamics.

Abstract

We try to establish a connection between the hadronic distributions, in proton-proton collisions at very high transverse momentum $p_{\mathrm{T}}$, obtained via perturbative QCD and the Tsallis non extensive statistics. Our motivation is that while the former is expected to be valid at extremely high momentum, due to asymptotic freedom, the latter has been very successful in describing experimental spectra over a wide range of momentum. Matching the non extensive statistics with the asymptotic $p_{\mathrm{T}}$ behaviour expected from QCD leads to the value of $q=1.25$.