Considering the general structure of the two point functions of quarks and gluons, we compute the free energy and pressure of a strongly magnetized hot and dense QCD matter created in heavy-ion collisions. In the presence of a strong magnetic field we found that the deconfined QCD matter exhibits a paramagnetic nature. One gets different pressures in directions parallel and perpendicular to the magnetic field due to the magnetization acquired by the system. We obtain both longitudinal and transverse pressures, and magnetization of hot deconfined QCD matter in the presence of the magnetic field. We have used hard thermal loop approximation for the heat bath. We obtained completely analytic expressions for pressure and magnetization under certain approximations. Various divergences appearing in free energy are regulated using appropriate counterterms. The obtained anisotropic pressure may be useful for a magnetohydrodynamics description of a hot and dense deconfined QCD matter produced in heavy-ion collisions.

In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. More specifically, Sec. 2 discusses mass of [Formula: see text] in the linear sigma model coupled to quarks at zero temperature. In Sec. 7, one-loop calculation of the anisotropic pressure are discussed in the presence of strong magnetic field. In Sec. 9, chiral transition and chiral susceptibility in the NJL model is discussed for a chirally imbalanced plasma in the presence of magnetic field using a Wigner function approach. Sections 10 discusses electrical conductivity and Hall conductivity of hot and dense hadron gas within Boltzmann approach and Sec. 11 deals with electrical resistivity of quark matter in presence of magnetic field. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12 and 15–17 of this article probe some aspects of this exciting field. In Sec. 12, analytical solutions of viscous Landau hydrodynamics in 1+1D are discussed. Section 15 deals with derivation of hydrodynamics from effective covariant kinetic theory. Sections 16 and 17 discuss hydrodynamics with spin and analytical hydrodynamic attractors, respectively. Transport coefficients together with their temperature- and density-dependence are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deal with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark–gluon plasma using Higgs–quark interaction and calculate the Higgs decays into quark and anti-quark, which shows a dominant on-shell contribution in the bottom-quark channel. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model to study hadron production from a dissipative quark–gluon plasma.

We consider weakly magnetized hot QED plasma comprising electrons and positrons.There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Considering the resummed fermion propagator in a weakly magnetized medium for the soft fermion and the Schwinger propagator for hard fermion, we calculate the soft contribution to the damping rate of hard photon. In weak field approximation the thermal and thermo-magnetic contributions to damping rate get separated out for each transverse dispersive mode. The total damping rate for each dispersive mode in presence of magnetic field is found to be reduced than that of the thermal one. This formalism can easily be extended to QCD plasma. * ritesh.ghosh@saha.ac.in

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