Non-extensivity of the QCD pT-spectra

We 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 are 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 momenta. Matching the non-extensive statistics with the asymptotic $ p_{\mathrm{T}}$ behaviour expected from QCD leads to the value of $ q=1.25$.