Motivated by the good Tsallis fits to the high-pT spectra in pp collisions at the LHC, we study the relativistic hard-scattering model and obtain an approximate analytical expression for the differential hard-scattering cross section at eta ~ 0. The
power-law behaviour of the transverse spectra, in the form of dsigma/dpT^2 propto 1/pT^n, gives a power index n in the range of 4.5-5.5 for jet production as predicted by pQCD, after the dependencies of the structure functions and the running coupling constant are properly taken into account. The power indices for hadron production n are slightly greater than those for jet production.
Phenomenological Tsallis fits to the CMS, ATLAS, and ALICE transverse momentum spectra of hadrons for pp collisions at LHC were recently found to extend over a large range of the transverse momentum. We investigate whether the few degrees of freedom
in the Tsallis parametrization may arise from the relativistic parton-parton hard-scattering and related processes. The effects of the multiple hard-scattering and parton showering processes on the power law are discussed. We find empirically that whereas the transverse spectra of both hadrons and jets exhibit power-law behavior of 1/pT^n at high pT, the power indices n for hadrons are systematically greater than those for jets, for which n~4-5.
Phenomenological Tsallis fits to the CMS and ATLAS transverse spectra of charged particles were found to extend for p_T from 0.5 to 181 GeV in pp collisions at LHC at sqrt{s}=7 TeV, and for p_T from 0.5 to 31 GeV at sqrt{s}=0.9 TeV. The simplicity of
the Tsallis parametrization and the large range of the fitting transverse momentum raise questions on the physical meaning of the degrees of freedom that enter into the Tsallis distribution or q-statistics.
