In this work, we address the problem of longitudinal spin polarization of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Λ</mi></math> hyperons produced in relativistic heavy-ion collisions. We combine a relativistic kinetic-theory framework that includes spin degrees of freedom treated in a classical way with the freeze-out parametrization used in previous investigations. The use of the kinetic theory allows us to incorporate dissipative corrections (due to the thermal shear and gradients of thermal vorticity) into the Pauli-Lubanski vector that determines spin polarization and can be directly compared with the experimental data. As in earlier similar studies, it turns out that a successful description of data can only be achieved with additional assumptions—in our case, they involve the use of projected thermal vorticity and a suitably adjusted time for spin relaxation (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>τ</mi><mi>s</mi></msub></math>). From our analysis, we find that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>τ</mi><mi>s</mi></msub><mo>∼</mo><mn>5</mn></mrow><mspace width="4pt"></mspace><mrow><mi>fm</mi><mo>/</mo><mi>c</mi></mrow></math>, which is comparable with other estimates.

India

Soham Banerjee

Poland

Samapan Bhadury

Wojciech Florkowski

Amaresh Jaiswal

Radoslaw Ryblewski

Longitudinal spin polarization in a thermal model with dissipative corrections

We extend the derivation of second-order relativistic viscous hydrodynamics to incorporate the effects of baryon current, a nonvanishing chemical potential, and a realistic equation of state. Starting from a microscopic quantum theory, we employ a quasiparticle approximation to describe the evolution of hydrodynamic degrees of freedom and establish its connection to the Wigner formalism. Using methods from relativistic kinetic theory, we perform a second-order expansion to derive a closed set of equations for the components of the stress-energy tensor and the baryon current. The resulting transport coefficients, which depend on the equation of state, are obtained through a unified prescription that ensures thermodynamic consistency.

Asaad Daher

Leonardo Tinti

Quasiparticle second-order dissipative hydrodynamics at finite chemical potential

We present analytical solution of relativistic hydrodynamics for a system having cylindrical symmetry with boost-invariant longitudinal expansion and Hubble-like transverse expansion. We also consider analytical solution for Hubble-like spherically expanding system. For these two cases, we calculate analytical expression for transverse momentum spectra of hadrons, at constant temperature freeze-out hypersurface using Cooper–Frye prescription. We compare our results for transverse momentum spectra with experimental results from Large Hadron Collider and CERN SPS where one expects cylindrical and spherical geometry of the fireball, respectively. In the case of low-energy collisions with spherical geometry, we calculate rapidity spectra and compare with the results from CERN SPS.

Mahammad Ali

Deeptak Biswas

Italy

Sushant Singh

Hadron momentum spectra from analytical solutions of relativistic hydrodynamics

In this study, we analyze the transport properties of the quark-gluon plasma (QGP), focusing on bulk (<math><mi>ζ</mi></math>) and shear (<math><mi>η</mi></math>) viscosities at vanishing chemical potential. To describe the QGP, we employ a quasiparticle model for quarks along with Gribov’s prescription for gluons, which effectively captures nonperturbative dynamics. The Gribov parameter <math><msub><mi>γ</mi><mi>G</mi></msub></math> and the dynamical mass <math><msub><mi>m</mi><mi>g</mi></msub></math> are obtained by solving the one-loop gap equation in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> renormalization scheme and further using lattice QCD data for the equation of state (EOS) of pure gluonic matter. The interaction between quarks and gluons is reflected in the quark quasimass <math><msub><mi>m</mi><mi>q</mi></msub></math>, again obtained using lattice EOS data for (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD. Our primary goal is to investigate the influence of quasiquarks on the transport coefficients of QGP. Interestingly, we find a substantial decrease in the scaled transport coefficients with rising temperatures within the range (<math><mn>1</mn><mo>≤</mo><mi>T</mi><mo>/</mo><msub><mi>T</mi><mi>c</mi></msub><mo>≤</mo><mn>3.5</mn></math>).

Sadaf Madni

Arghya Mukherjee

Najmul Haque

Shear and bulk viscosity of the quark-gluon plasma with Gribov gluons and quasiparticle quarks

The strongly interacting matter created in relativistic heavy-ion collisions possesses several conserved quantum numbers, such as baryon number, strangeness, and electric charge. The diffusion process of these charges can be characterized by a diffusion matrix that describes the mutual influence of the diffusion of various charges. We derive the Kubo relations for evaluating diffusion coefficients as elements of a diffusion matrix. We further demonstrate that in the weak coupling limit, the diffusion matrix elements obtained through Kubo relations reduce to those obtained from kinetic theory with an appropriate identification of the relaxation times. We illustrate this evaluation in a toy model of two interacting scalar fields with two conserved charges.

Sourav Dey

Hiranmaya Mishra

Diffusion coefficient matrix for multiple conserved charges: a Kubo approach

Equal-time commutators of different components of the energy-momentum tensor at spatially separated points are calculated for a relativistic quantum Fermi gas at finite temperature and density. Different definitions of such components, also known as different pseudogauges, are used and smeared with a Gaussian profile characterized by the width <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>. In this way, we introduce observables that may represent measurements of energy and momentum in a spatial region of size <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>. We find that the obtained commutators are sensitive to the pseudogauge chosen if the probed systems or the spatial separation are small. The pseudogauge dependence is expected as different quantum operators are analyzed in this case. On the other hand, we find that for sufficiently large probed systems or with large separation, the studied commutators are pseudogauge independent.

Energy-momentum correlators of fermions at finite temperature and density

In the present work, we derive a linearly stable and causal theory of relativistic third-order viscous hydrodynamics from the Boltzmann equation with relaxation-time approximation. We employ viscous correction to the distribution function obtained using a Chapman-Enskog like iterative solution of the Boltzmann equation. Our derivation highlights the necessity of incorporating a new dynamical degree of freedom, specifically an irreducible tensor of rank three, within this framework. This differs from the recent formulation of causal third-order theory from the method of moments which requires two dynamical degrees of freedom: an irreducible third-rank and a fourth-rank tensor. We verify the linear stability and causality of the proposed formulation by examining perturbations around a global equilibrium state.

Pushpa Panday

Binoy Krishna Patra

Causal third-order viscous hydrodynamics within relaxation-time approximation

We consider thermodynamics of the Universe within a quasiparticle approach where the collective dynamics of a system is governed by the thermal mass of the constituents. The spacetime dependence of this thermal mass leads to a negative contribution to the pressure and a positive contribution to the energy density, similar to the effect due to dark energy. We propose a mechanism based on thermodynamic arguments to quantify this contribution from the thermal vacuum of the system. For a sufficiently large spacetime variation of the thermal mass, the effective pressure can become negative and could mimic a dark energy equation of state. We validate our framework using results from renormalizable interacting scalar field theory and demonstrate an application on QCD axion.

Quasiparticle cosmology

Bhatnagar–Gross–Krook (BGK) collision kernel is employed in the Boltzmann equation to formulate relativistic dissipative hydrodynamics. In this formulation, we find that there remains freedom of choosing a matching condition that affects the scalar transport in the system. We also propose a new collision kernel which, unlike BGK collision kernel, is valid in the limit of zero chemical potential and derive relativistic first-order dissipative hydrodynamics using it. We study the effects of this new formulation on the coefficient of bulk viscosity.

Romania

Pracheta Singha

Canada

Relativistic BGK hydrodynamics

The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local redistribution of such quantities (with global energy, linear momentum, and angular momentum remaining unchanged). This arbitrariness is described in recent literature as the pseudogauge freedom or symmetry. In this letter, we analyze several pseudogauges used to formulate the relativistic hydrodynamics of particles with spin <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> and conclude that the canonical version of the spin tensor has an advantage over other forms as only the canonical definition defines the spin operators that fulfill the SO(3) algebra of angular momentum. This result sheds new light on the results encountered in recent papers demonstrating pseudogauge dependence of various physical quantities. It indicates that for spin-polarization observables, the canonical version is fundamentally better suited for building a connection between theory and experiment.