Statistical Approaches to High Energy Physics: Chemical and Thermal Freeze-Outs

• Main Authors: Jean Cleymans, Masimba Wellington Paradza
• Format: Article
• Language: English
• Published: MDPI AG 2020-12-01
• Series: Physics
• Subjects: statistical mechanics; thermal model; high energy physics
• Online Access: https://www.mdpi.com/2624-8174/2/4/38

We present an overview of a proposal in relativistic proton-proton (<inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula>) collisions emphasizing the thermal or kinetic freeze-out stage in the framework of the Tsallis distribution. In this paper we take into account the chemical potential present in the Tsallis distribution by following a two step procedure. In the first step we used the redudancy present in the variables such as the system temperature, <i>T</i>, volume, <i>V</i>, Tsallis exponent, <i>q</i>, chemical potential, <inline-formula><math display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>, and performed all fits by effectively setting to zero the chemical potential. In the second step the value <i>q</i> is kept fixed at the value determined in the first step. This way the complete set of variables <inline-formula><math display="inline"><semantics><mrow><mi>T</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>V</mi></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> can be determined. The final results show almost no (or at best a very weak) energy dependence in <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula> collisions at the centre-of-mass energy <inline-formula><math display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>20</mn></mrow></semantics></math></inline-formula> TeV to 13 TeV. The chemical potential <inline-formula><math display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> at kinetic freeze-out shows a steep increase with beam energy. This considerably simplifies the description of the thermal freeze-out stage in <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula> collisions as the values of <i>T</i> and of the freeze-out radius <i>R</i> remain constant to a good approximation over a wide range of beam energies.