Multiplicity Dependence of Hadron Spectra in Proton-proton Collisions at LHC Energies and Super-statistics

In this paper, transverse momentum spectra of pi+, K+ and p measured at fix event-multiplicities and \sqrt s = 0.9, 2.76 and 7 TeV collision energies by the CMS Collabotaion are shown to fit the Tsallis-distribution. It is found that the power of the distribution shows a double-logarithmic dependence on the event-multiplicity N, while the T parameter depends linearly on N. A similar double-logarithmic dependence of the q parameter of pi0 spectra on the collision energy \sqrt{s} is found too. It is also shown that event-by-event fluctuations of the multiplicity N and the total E_T energy going into the transverse region can be the reason for the emergence of the Tsallis distribution in high-energy proton-proton collisions.