Applications of extensive and non-extensive statistics to high energy physics

Paradza, Masimba Welligton

Applications of extensive and non-extensive statistics to high energy physics

Doctoral Thesis

2021

Abstract

Heavy ion collisions produce nuclear matter at high temperatures and densities, to gain insights into this nuclear matter, we make use of statistical and thermal models to analyse the matter in the final state. A significant number of recent publications have shown that fits based on the Tsallis distribution give a good description of transverse momentum distributions measured at the Large Hadron Collider in p − p collisions. We set out to determine systematic behaviour of the parameters obtained and to gain theoretical insight in these. A detailed analysis is presented of the precise values of the Tsallis parameters obtained in p − p collisions for identified particles, pions, kaons and protons at the LHC at three beam energies √ s = 0.9, 2.76 and 7 TeV. Interpolated data at √ s = 5.02 TeV have also been included. It is shown that the Tsallis formula provides reasonably good fits to the pT distributions in p − p collisions at the LHC using three parameters dN/dy, T0 and q. However, the parameters T0 and q depend on the particle species and are different for pions, kaons and protons. As a consequence there is no mT scaling and also no universality of the parameters for different particle species. The thermodynamic parameters like energy density, pressure, entropy density, temperature and particle density are determined from the transverse momentum distributions of charged particles in Pb-Pb and Xe-Xe collisions at the LHC. The results show a clear increase with the centrality and the beam energy in all parameters. It is determined that in the final freeze-out stage the energy density reaches a value of about 0.039 GeV/fm3 for the most central collisions at √ sNN = 5.02 TeV. This is less than that at chemical freeze-out where the energy density is about 0.36 GeV/fm3 . This decrease approximately follows a T 4 law. The results for the pressure and entropy density are presented for each centrality class at √ sNN = 2.76 and 5.02 TeV for Pb-Pb collisions as well as at √ sNN = 5.44 TeV for Xe-Xe collisions. An analysis is made of the particle composition (hadrochemistry) of the final state in proton-proton p − p, proton-lead p−Pb and lead-lead Pb-Pb collisions as a function of the charged particle multiplicity (dNch/dη). The thermal model is used to determine the chemical freeze-out temperature as well as the radius and strangeness saturation factor γs . Abstract Three different ensembles are used in the analysis namely, the grand canonical ensemble, the canonical ensemble with exact strangeness conservation and the canonical ensemble with exact baryon number, strangeness and electric charge conservation. It is shown that for high multiplicities (at least 20 charged hadrons in the mid-rapidity interval considered) the three ensembles lead to the same results. Finally, most of the results discussed in this thesis have been published before in [1, 2, 3, 4, 5], in addition, results on Xe-Xe and chemical potential analysis are new in this thesis. I read and reviewed over 200 articles of which 130 made it into the final thesis. This extensive literature review allowed me to gain a broad overview of the basics of high energy physics, extensive and non-extensive statistics together with their applications in this field. I also became well-informed of the current research and this helped me to conceptualise and formulate the various research questions in his thesis. I searched for data using the references from the various articles and came up with a large data set covering as much scope as possible, representative enough to adequately address the questions I have raised. From the literature, I developed several macros to fit the data. To derive insights and to make a meaningful analysis of the data, I developed a methodology to systematically organize the data in pursuit of the research objectives, and to plot the relevant graphs from this large sample of data. From this, I prepared results tables together with the many relevant graphs presented in this thesis. I analysed the results in the tables and the figures and critically reflected on their meaning and finally derived the conclusions. After conducting the analysis, interpreting the results, I prepared the text for the draft manuscripts for all articles published. This thesis is written in a traditional way, so that I can expand on the details than in the articles. In the publications, I included tables and graphs depending on what I needed to highlight, and this thesis brings everything together. All this work was achieved under the guidance of my supervisors. The names on the articles do not appear in alphabetical order.

Keywords

Phsysics

Reference:

Collections

PhD / Doctoral

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