Abstract
The thermalization of the particles produced in collisions of small size objects can be achieved by quantum entanglement of the partons of the initial state as it was analyzed recently in proton-proton collisions. We extend such study to Pb-Pb collisions and to different multiplicities of proton-proton collisions. We observe that, in all cases, the effective temperature is approximately proportional to the hard scale of the collision. We show that such relation between the thermalization temperature and the hard scale can be explained as a consequence of the clustering of the color sources. The fluctuations on the number of parton states decreases with multiplicity in Pb-Pb collisions as far as the width of the transverse momentum distributions decreases, contrary to the p-p case. We relate these fluctuations to the temperature time fluctuations by means of a Langevin equation for the white noise due to the quench of a hard parton collision.
Highlights
The presence of an exponential shape in the transversemomentum distribution (TMD) of the produced particles in collisions of small objects together with the approximate thermal abundances of the hadron yields constitutes an indicative sign of thermalization
The effective temperature obtained from the TMD of the particles produced in the collision depends on the momentum transfer; that is, it constitutes an ultraviolet cutoff of the quantum modes resolved by the collision
We show that the TMDs of both collisions at different multiplicities can be fitted by the sum of an exponential plus a powerlike function, characterized by a thermal-like temperature, Tth, and a temperature scale, Th, respectively
Summary
The presence of an exponential shape in the transversemomentum distribution (TMD) of the produced particles in collisions of small objects together with the approximate thermal abundances of the hadron yields constitutes an indicative sign of thermalization. In this article we further explore the relation between parton entanglement and thermalization by studying p-p and Pb-Pb collisions at different multiplicities. The power index n describing the hard spectrum behaves differently in p-p and Pb-Pb collisions, showing the different behavior of the transverse-momentum fluctuations This behavior and the relation between Tth and Th can be naturally explained in the clustering of color sources. To study the dependence on the multiplicity of Tth and Th we have used the transverse-m√omentum distribution of KS0 produced in p-p collisions at s = 7 TeV in the range up to pt 10 GeV/c [13]. In Ref. [1], the thermal component transverse-momentum distribution in p-p ocfollcihsiaorngseda-th√adsro=n
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