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We investigate magnetic field $(eB)$ dependence of constituent quark mass, the longitudinal and transverse pressure as well as the magnetization and magnetic susceptibility of strongly interacting quark matter. We employ the two-flavour Polyakov Nambu--Jona-Lasinio model with the inclusion of the anomalous magnetic moment (AMM) of the quarks at finite temperature $(T)$ and finite quark chemical potential $(\mu_q)$ capturing different stages of chiral phase transition. We find that the transverse pressure, magnetization and magnetic susceptibility become highly oscillatory for large values of $eB$ in the chiral symmetry broken phase. However the oscillations cease to occur at higher values of $T$ and $\mu_q$ when chiral symmetry is (partially) restored and the anisotropic nature of the pressure becomes significant even at smaller values of $eB$. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis of the transition temperature we observe that the variations of transverse pressure, magnetization and magnetic susceptibility are significantly modified in the vicinity of the chiral transition temperature. Furthermore, above the chiral transition temperature the magnetic susceptibility is found to remain positive for a wide range of $eB$ indicating a paramagnetic character of the strongly interacting quark matter. Finally, we have also examined the magnetism of strongly interacting matter in the quarkyonic phase. The obtained results could be useful for a magnetohydrodynamic evolution of hot and dense matter created in heavy-ion collisions., Comment: Version Published in Physical Review D

The one-loop self-energy of the neutral ρ meson is obtained for the effective ρππ and ρNN interaction at finite temperature and density in the presence of a constant background magnetic field of arbitrary strength. In our approach, the eB-dependent vacuum part of the self-energy is extracted by means of dimensional regularization where the ultraviolet divergences corresponding to the pure-vacuum self-energy manifest as the pole singularities of gamma as well as Hurwitz zeta functions. This improved regularization procedure consistently reproduces the expected results in the vanishing magnetic field limit and can be used quite generally in other self-energy calculations dealing with arbitrary magnetic field strength. In the presence of the external magnetic field, the general Lorentz structure for the in-medium vector boson self-energy is derived, which can also be implemented in the case of the gauge bosons such as photons and gluons. It has been shown that with vanishing perpendicular momentum of the external particle essentially two form factors are sufficient to describe the self-energy completely. Consequently, two distinct modes are observed in the study of the effective mass, dispersion relations and the spectral function of ρ0 where one of the modes possesses twofold degeneracy. For large baryonic chemical potential, it is observed that the critical magnetic field required to block the ρ0→π+π- decay channel increases significantly with temperature. However, in the case of smaller values reaching down to vanishing chemical potential, the critical field follows the opposite trend.

A phenomenological pion-nucleon interaction is used to obtain pionic mass modification in presence of constant homogeneous magnetic field background at finite temperature and chemical potential in the real time formalism of thermal field theory. The magnetically modified propagator in its complete form is used to obtain the one loop self-energy for pions. For charged pions we find that the effective mass increases with the magnetic field at given temperature and chemical potential. Since the transverse momentum of charged pion is quantized and its contribution to Dyson-Schwinger Equation is large compared to the loop correction, the charged pion mass remains constant with both temperature and chemical potential for a given landau level. In order to unveil the role of the real part of the self-energy, we also calculate the effective mass neglecting the trivial shift. The effective mass for charged pions shows an oscillatory behavior which is attributed to the thermal contribution of the self-energy. It is argued that the magnetic field dependent vacuum contribution to the self-energy influences the behavior of the effective mass both qualitatively and quantitatively. We also find that very large field is necessary for neutral pions to condense., 16 pages, 6 figures

The self-energy of the $\mathrm{\ensuremath{\Delta}}$ baryon is evaluated at a finite temperature and density using the real-time formalism of thermal field theory. The Dyson-Schwinger equation is used to get the exact thermal propagator followed by the spectral function of $\mathrm{\ensuremath{\Delta}}$. The $\ensuremath{\pi}N$ scattering cross section obtained using an explicit $\mathrm{\ensuremath{\Delta}}$ exchange is normalized to the experimental data in the vacuum, and its medium modification is implemented by means of the exact thermal propagator. A significant suppression of the peak of the cross section is observed at a higher temperature and baryon density. Effects on the mean relaxation time of nucleons and the temperature dependence of the shear viscosity of a pion nucleon gas are demonstrated.

We calculate the rho meson mass in a weak magnetic field using effective $\rho\pi\pi$ interaction. It is seen that both $\rho^0$ and $\rho^\pm$ masses decrease with the magnetic field in vacuum. $\rho$ meson dispersion relation has been calculated and shown to be different for $\rho^0$ and $\rho^\pm$. We also calculate the $\rho\pi\pi$ decay width and spectral functions of $\rho^0$ and $\rho^\pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.

The drag and diffusion coefficients of the ${\mathrm{\ensuremath{\Lambda}}}_{c}(2286\text{ }\text{ }\mathrm{MeV})$ have been evaluated in the hadronic medium which is expected to be formed in the later stages of the evolving fireball produced in heavy ion collisions at RHIC and LHC energies. The interactions between the ${\mathrm{\ensuremath{\Lambda}}}_{c}$ and the hadrons in the medium have been derived from an effective hadronic Lagrangian, as well as from the scattering lengths obtained in the framework of heavy baryon chiral perturbation theory ($\mathrm{HB}\ensuremath{\chi}\mathrm{PT}$). In both the approaches, the magnitude of the transport coefficients turn out to be significant. A larger value is obtained in the former approach with respect to the latter. Significant values of the coefficients indicate a substantial amount of interaction of the ${\mathrm{\ensuremath{\Lambda}}}_{c}$ with the hadronic thermal bath. Furthermore, the transport coefficients of the ${\mathrm{\ensuremath{\Lambda}}}_{c}$ are found to be different from the transport coefficients of the $D$ meson. The present study indicates that the hadronic medium has a significant impact on the ${\mathrm{\ensuremath{\Lambda}}}_{c}/D$ ratio in heavy ion collisions.

We investigate the effect of the medium on the thermal conductivity of a pion gas out of chemical equilibrium by solving the relativistic transport equation in the Chapman-Enskog and relaxation time approximations. Using an effective model for the pi-pi cross-section involving rho and sigma meson exchange, medium effects are incorporated through thermal one-loop self-energies. The temperature dependence of the thermal conductivity is observed to be significantly affected.

The bulk and shear viscosities of a pion gas are obtained by solving the relativistic transport equation in the Chapman-Enskog approximation. In-medium effects are introduced in the $\ensuremath{\pi}\ensuremath{\pi}$ cross section through one-loop self-energies in the propagator of the exchanged $\ensuremath{\rho}$ and $\ensuremath{\sigma}$ mesons. The effect of early chemical freeze-out in heavy ion collisions is implemented through a temperature-dependent pion chemical potential. These are found to affect the temperature dependence of the bulk and shear viscosities significantly.