We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in the presence of a nontrivial background such as a hot magnetized medium. This is applicable to both QED and QCD. The hard thermal loop approximation has been used for the heat bath. We have also examined transformation properties of the effective fermion propagator under some of the discrete symmetries of the system. Using the effective fermion propagator we have analyzed the fermion dispersion spectra in a hot magnetized medium along with the spinor for each fermion mode obtained by solving the modified Dirac equation. The fermion spectra is found to reflect the discrete symmetries of the two-point functions. We note that for a chirally symmetric theory the degenerate left-and right-handed chiral modes in vacuum or in a heat bath get separated and become asymmetric in the presence of a magnetic field without disturbing the chiral invariance. The obtained general structure of the two-point functions is verified by computing the three-point function, which agrees with the existing results in oneloop order. Finally, we have computed explicitly the spectral representation of the two-point functions which would be very important to study the spectral properties of the hot magnetized medium corresponding to QED and QCD with background magnetic field.

We have computed the hard dilepton production rate from a weakly magnetized deconfined QCD medium within one-loop photon self-energy by considering one hard and one thermomagnetic resummed quark propagator in the loop. In the presence of the magnetic field, the resummed propagator leads to four quasiparticle modes. The production of hard dileptons consists of rates when all four quasiquarks originating from the poles of the propagator individually annihilate with a hard quark coming from a bare propagator in the loop. Besides these, there are also contributions from a mixture of pole and Landau cut part. In weak field approximation, the magnetic field appears as a perturbative correction to the thermal contribution. Since the calculation is very involved, for a first effort as well as for simplicity, we obtained the rate up to first order in the magnetic field, i.e., O[(eB)], which causes a marginal improvement over that in the absence of magnetic field. * aritra.das@saha.ac.in † nhaque@niser.ac.in

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 calculate neutral pion mass in presence of an external arbitrary magnetic field in the framework of linear sigma model coupled to quark (LSMq) at zero temperature. We find non-monotonic behavior of pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak field approximation. I. INTRODUCTIONIn heavy-ion collisions (HIC) experiments, a very strong anisotropic magnetic field (∼ 10 19 Gauss) is generated in peripheral collisions due to the relative motion of the colliding ions [1-5] and the direction of the generated magnetic field is perpendicular to the reaction plane. Apart from the HIC, finite magnetic field is also involved in the interior of dense astrophysical objects like compact stars, magnetars [6] and also in the early universe. The effects of such magnetic fields on fundamental particles cannot be neglected and the detailed understanding of the effects on the elementary particles is essential at fundamental levels.One of such effects is the behavior of meson masses as a function of the strength of the magnetic field. The study of magnetic field dependent meson masses is a subject of active research. In Ref.[7], the authors have studied light mesons, namely charged, neutral pions (π ± , π 0 ), rho mesons (ρ ± , ρ 0 ), masses in the presence external electromagnetic field in the framework of lattice quantum chromodynamics (LQCD) and have shown that the magnetic field dependent neutral pion mass decreases with the magnetic field strength.Apart from LQCD calculations, various effective QCD models have been used to study the properties of meson masses in presence of magnetic field. This includes chiralperturbation theory [8,9], pseudoscalar(PS) and pseudovector(PV) pion-nucleon interaction model [10,11], Nambu-Jona Laisino(NJL) model and its extension [12][13][14][15][16], Polyakov loop extension of NJL (PNJL) model [17,18], PQM model [19,20], quark-meson model [21][22][23][24][25].The linear sigma model (LSM) is one of oldest, simplest model in pre-QCD era originally proposed by Gell-Mann and Lévy [26] to describe pion-nucleon interaction. Many global symmetries of QCD is seen to be exhibited * aritra.das@saha.ac.in † nhaque@niser.ac.in