<p>At nonzero temperatures, the deconfining phase transition can be analyzed using an effective matrix model to characterize the change in holonomy. The model includes gluons and two-dimensional ghost fields in the adjoint representation, or “teens.” As ghosts, the teen fields are responsible for the decrease of the pressure as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">→</mo><msub><mi>T</mi><mi>d</mi></msub></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math> the transition temperature for deconfinement. Using the solution of this matrix model for a large number of colors, the parameters of the teen fields are adjusted so that the expectation value of the Polyakov loop is close to the values from the lattice. The shear, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>, and bulk, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math>, viscosities are computed at nonzero holonomy to leading logarithmic order in weak coupling. In the pure glue theory, the value of the Polyakov loop is relatively large in the deconfined phase, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≈</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math>. Consequently, if <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> is the entropy density, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math> decreases as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mo stretchy="false">→</mo><msub><mi>T</mi><mi>d</mi></msub></math>, it is still well above the conformal bound. In contrast, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi><mo>/</mo><mi>s</mi></math> is largest at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>d</mi></msub></math>, comparable to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math>, then falls off rapidly with increasing temperature and is negligible by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>2</mn><msub><mi>T</mi><mi>d</mi></msub></math>.</p>

India

Manas Debnath

United States

Ritesh Ghosh

Najmul Haque

Japan

Yoshimasa Hidaka

Robert D. Pisarski

Shear and bulk viscosity for a pure glue theory using an effective matrix model

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

Amaresh Jaiswal

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

In this work, we investigate the momentum-dependent drag and diffusion coefficient of heavy quarks (<math><mi>HQs</mi></math>) moving in the quark-gluon plasma background. The leading order scattering amplitudes required for this purpose have been obtained using the Gribov-Zwanziger propagator for the mediator gluons to incorporate the nonperturbative effects relevant to the phenomenologically accessible temperature regime. The drag and diffusion coefficients so obtained have been implemented to estimate the temperature and momentum dependence of the energy loss of the HQ as well as the temperature dependence of the specific shear viscosity (<math><mi>η</mi><mo>/</mo><mi>s</mi></math>) of the background medium. Our results suggest a higher energy loss of the propagating HQ compared to the perturbative estimates, whereas the <math><mi>η</mi><mo>/</mo><mi>s</mi></math> is observed to comply with the AdS/CFT estimation over a significantly wider temperature range compared to the perturbative expectation.

 Sumit

Binoy Krishna Patra

Heavy quark dynamics via the Gribov-Zwanziger approach

Gribov–Zwanziger prescription in Yang–Mills theory improves the infrared dynamics. In this work, we study the static potential of a heavy quark-antiquark pair with the HTL resummed perturbation method within the Gribov–Zwanziger approach at finite temperature. The real and imaginary parts of the heavy quarkonium complex potential are obtained from the one-loop effective static gluon propagator. The one-loop effective gluon propagator is obtained by calculating the one-loop gluon self-energies containing the quark, gluon, and ghost loop. The gluon and ghost loops are modified in the presence of the Gribov parameter. We also calculate the decay width from the imaginary part of the potential. We also discuss the medium effect of heavy quarkonium potential with the localized action via auxiliary fields.

The complex heavy quarkonium potential with the Gribov–Zwanziger action

We compute the heavy quarkonium complex potential in a magnetic field of arbitrary strength generated in the relativistic heavy-ion collision. First, the one-loop gluon polarization tensor is obtained in the presence of an external, constant, and homogeneous magnetic field using the Schwinger proper time formalism in Euclidean space. The gluon propagator is computed from the gluon polarization tensor, and it is used to calculate the dielectric permittivity in the presence of the magnetic field. The modified dielectric permittivity is then used to compute the heavy quarkonium complex potential. We find that the heavy quarkonium complex potential is anisotropic in nature, which depends on the angle between the quark-antiquark (<math><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover></math>) dipole axis and the direction of the magnetic field. We discuss the effect of the magnetic field strength and the angular orientation of the dipole on the heavy quarkonium potential. We discuss how the magnetic field influences the thermal widths of quarkonium states. Further, we also discuss the limitation of the strong-field approximation as done in literature in the light of heavy-ion observables, as the effect of the magnetic field is very nominal to the quarkonium potential.

Jobin Sebastian

South Korea

Lata Thakur

Hiranmaya Mishra

Heavy quarkonia in QGP medium in an arbitrary magnetic field

The screening masses of mesons provide a gauge invariant and definite order parameter of chiral symmetry restoration. Different mesonic correlation lengths for flavor non-singlets, at least up to NLO, are well-defined gauge invariant physical quantities calculated earlier using the perturbative resummation techniques. The NLO perturbative results match the available non-perturbative lattice QCD results at the high-temperature regime. We have studied the spatial correlation lengths of various mesonic observables using the non-perturbative Gribov resummation, both for quenched QCD and <math><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></math> flavor QCD. The study follows the analogies with the NRQCD effective theory, a well-known theory for studying heavy quarkonia at zero temperature.

QCD mesonic screening masses using Gribov quantization

We study the neutral pion mass in the presence of an external arbitrary magnetic field in the framework of the linear sigma model coupled to quarks to a quark at finite temperature. In doing so, we have calculated the pion self-energy, constructed the dispersion equation via resummation, and solved the dispersion relation at zero three-momentum limit. In calculating the pion mass, we have included meson self-coupling’s thermal and magnetic contribution and approximate chiral order parameter <math><msub><mi>v</mi><mn>0</mn></msub></math>. We report that the <math><msup><mi>π</mi><mn>0</mn></msup></math> mass decreases with the magnetic field and increases with temperature.

Aritra Das

Neutral pion mass in a warm magnetized medium within the linear sigma model coupled to quarks framework

Using the hard-thermal-loop (HTL) resummation in real-time formalism, we study the next-to-leading order (NLO) quark self-energy and corresponding NLO dispersion laws. In NLO, we have replaced all the propagators and vertices with the HTL-effective ones in the usual quark self-energy diagram. Additionally, a four-point vertex diagram also contributes to the quark NLO self-energy. We calculate the usual quark self-energy diagram and the four-point vertex diagram separately. Using those, we express the NLO quark self-energy in terms of the three- and four-point HTL-effective vertex functions. Using the Feynman parametrization, we express the integrals containing the three- and four-point HTL effective vertex functions in terms of the solid angles. After completing the solid angle integrals, we numerically calculate the momentum integrals in the NLO quark self-energy and plot them as a function of the ratio of momentum and energy. Using the NLO quark self-energy, we plot the NLO correction to dispersion laws.

Binoy Patra

NLO quark self-energy and dispersion relation using the hard thermal loop resummation

We investigate the nature of the complex retarded potential of a heavy quarkonium moving in a hot and dense static deconfined nuclear medium. The well-known concept of the retarded potential in electrodynamics is extended to the context of the heavy-quark by modifying the static vacuum Cornell potential through Lorentz transformation to the static frame of the medium. The resulting potential in the vacuum is further corrected to incorporate the screening effect offered by the thermal medium. To do so, the retarded Cornell potential is modified by the dielectric function of the static quark-gluon plasma (QGP) medium. We present the numerical results for the real and imaginary parts of the potential along with the analytical expression of the potential approximated by a small velocity limit. Finally, we present the thermal width of quarkonia in the QGP medium derived using the imaginary part of the potential and study its dependence on velocity and temperature.

Mohammad Yousuf Jamal

Liénard-Wiechert potential of a heavy quarkonium moving in QGP medium

The heavy quark momentum diffusion coefficient (κ) is one of the most essential ingredients for the Langevin description of heavy quark dynamics. In the temperature regime relevant to the heavy ion collision phenomenology, a substantial difference exists between the lattice estimations of κ and the corresponding leading order (LO) result from the hard thermal loop (HTL) perturbation theory. Moreover, the indication of poor convergence in the next-to-leading order (NLO) perturbative analysis has motivated the development of several approaches to incorporate the non-perturbative effects in the heavy quark phenomenology. In this work, we estimate the heavy quark diffusion coefficient based on the Gribov-Zwanziger prescription. In this framework, the gluon propagator depends on the temperature-dependent Gribov mass parameter, which has been obtained self-consistently from the one-loop gap equation. Incorporating this modified gluon propagator in the analysis, we find a reasonable agreement with the existing lattice estimations of κ within the model uncertainties.