  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 $q=1.25$.
