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

Abstract

In this paper, transverse momentum spectra of π + , K + and p measured at fix event-multiplicities and √ s = 0.9, 2.76 and 7 TeV collision energies by the CMS Collabotaion are shown to fit the Tsallisdistribution. 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 π 0 spectra on the collision energy √ 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 protonproton collisions.

Using the Tsallis distribution for hadron spectra in pp collisions: Pions and quarkonia at s=5−13000 G

“…Besides the temperature T and chemical potential µ it has an additional parameter q and reduces to BGD in the limit q → 1. TD can be considered as a result of averaging of the temperature fluctuations in the BGD, where q − 1 characterizes the strength of these fluctuations [20] (for other interpretations, see [34,35]). The relation of TD with the QCD hard-scattering formulas is discussed in [30,31].…”

A ‘soft + hard’ model for heavy-ion collisions

“…If in each nucleus-nucleus collision, hadrons stemming from soft processes have either Boltzmann-Gibbs or micro-canonical distribution, however, hadron multiplicity fluctuates according to the negative-binomial distribution, then the cut-power law function Eq. ( 2) emerges as the average hadron spectrum [12,19,20,21,28,31,33,40,41]. If q → 1, Eq.…”

“…Once hard hadron yields (obtained in the (i) and (ii) scenarios) are subtracted from the measured transverse hadron spectra, we describe the remaining soft yields in the often used super-statistical framework [12,19,20,21,28,31,33,40,41]. In this paper, we use the interpretation in which, the cut-power law shape of the soft hadron distribution originates from multiplicity fluctuations rather than from non-extensive entropy or transport [29,32].…”

Transverse Momentum Distributions at the LHC and Tsallis Thermodynamics

“…( 16) but not in Eq. (18). The inclusion of the factor m T leads to a more consistent interpretation of the variables q and T .…”