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Register a new userThermal Field Theory of the Tsallis statistics
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Classical and quantum Tsallis distributions have been widely used in many branches of natural and social sciences. But, the quantum field theory of the Tsallis distributions is relatively a less explored arena. In this article we derive the expression for the thermal two-point functions for the Tsallis statistics with the help of the corresponding statistical mechanical formulations. We show that the quantum Tsallis distributions used in the literature appear in the thermal part of the propagator much in the same way the Boltzmann-Gibbs distributions appear in the conventional thermal field theory. As an application of our findings, thermal mass of the real scalar bosons subjected to phi^4 interaction has been calculated in the Tsallis statistics.
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We present an overview of a proposal in relativistic proton-proton ($pp$) 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 redundancy present in the variables such as the system temperature, $T$, volume, $V$, Tsallis exponent, $q$, chemical potential, $mu$, and performed all fits by effectively setting to zero the chemical potential. In the second step the value $q$ is kept fixed at the value determined in the first step. This way the complete set of variables $T, q, V$ and $mu$ can be determined. The final results show a weak energy dependence in $pp$ collisions at the centre-of-mass energy $sqrt{s}= 6$ GeV to 13 TeV. The chemical potential $mu$ at kinetic freeze-out shows an increase with beam energy. This simplifies the description of the thermal freeze-out stage in $pp$ collisions as the values of $T$ and of the freeze-out radius $R$ vary only mildly over a wide range of beam energies.
The scaling of charged hadron fragmentation functions to the Tsallis distribution for $0.01 lessapprox x lessapprox 0.2$ is presented for various $e^+e^-$ collision energies. A possible microcanonical generalisation of the Tsallis distribution is proposed, which gives good agreement with measured data up to $xapprox1$. The proposal is based on superstatistics and a $KNO$ like scaling of multiplicity distributions in $e^+e^-$ experiments.
The nature of dark matter (DM) and how it might interact with the particles of the Standard Model (SM) is one of greatest mysteries currently facing particle physics, and addressing these issues should provide some understanding of how the observed relic abundance was produced. One widely considered production mechanism, a weakly interacting massive particle (WIMP) produced as a thermal relic, provides a target cross section for DM annihilation into SM particles by solving the Boltzmann equation. In this thermal freeze-out mechanism, dark matter is produced in thermal equilibrium with the SM in the early universe, and drops out of equilibrium to its observed abundance as the universe cools and expands. In this paper, we study the impact of a generalized thermodynamics, known as Tsallis statistics and governed by a parameter $q$, on the target DM annihilation cross section. We derive the phase space distributions of particles in this generalized statistical framework, and check their thermodynamic consistency, as well as analyzing the impact of this generalization on the collisional term of the Boltzmann equation. We consider the case of an initial value of $q_0>1$, with $q$ relaxing to 1 as the universe expands and cools, and solve the generalized Boltzmann numerically for several benchmark DM masses, finding the corresponding target annihilation cross sections as a function of $q_0$. We find that as $q$ departs from the standard thermodynamic case of $q=1$, the collisional term falls less slowly as a function of $x = m_chi/T$ than expected in the standard case. We also find that the target cross section falls sharply from $sigma v simeq 2.2-2.6times10^{-26} textrm{cm}^3/textrm{s}$ for $q_0=1$ to, for example, $sigma v simeq 3times 10^{-34} textrm{cm}^3/textrm{s}$ for $q_0=1.05$ for a 100 GeV WIMP.
The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different $q$-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly present that the temperature where the mass cut-off starts, varies with the $q$-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of $q$ above approximately 1.13 all criticality disappear in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of $q$, disappears completely.
The study of higher-order moments of a distribution and its cumulants constitute a sensitive tool to investigate the correlations between the particle produced in high energy interactions. In our previous work we have used the Tsallis $q$ statistics, NBD, Gamma and shifted Gamma distributions to describe the multiplicity distributions in $pi ^-$ -nucleus and $p$ -nucleus fixed target interactions at various energies ranging from P$_{Lab}$ = 27 GeV to 800 GeV. In the present study we have extended our analysis by calculating the moments using the Tsallis model at these fixed target experiment data. By using the Tsallis model we have also calculated the average charged multiplicity and its dependence on energy. It is found that the average charged multiplicity and moments predicted by the Tsallis statistics are in much agreement with the experimental values and indicates the success of the Tsallis model on data from visual detectors. The study of moments also illustrates that KNO scaling hypothesis holds good at these energies.
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