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Register a new userGeneral structure of gauge boson propagator and its spectra in a hot magnetized medium
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Based on transversality condition of gauge boson self-energy we have systematically constructed the general structure of the gauge boson two-point functions using four linearly independent basis tensors in presence of a nontrivial background, i.e., hot magnetized material medium. The hard thermal loop approximation has been used for the heat bath to compute various form factors associated with the gauge bosons two point functions both in strong and weak field approximation. We have also analyzed the dispersion of a gauge boson (e.g., gluon) using the effective propagator both in strong and weak magnetic field approximation. The formalism is also applicable to QED. The presence of only thermal background leads to a longitudinal (plasmon) mode and a two-fold degenerate transverse mode. In presence of a hot magnetized background medium the degeneracy of the two transverse modes is lifted and one gets three quasiparticle modes. In weak field approximation one gets two transverse modes and one plasmon mode. On the other hand, in strong field approximation also one gets the three modes in Lowest Landau Level. The general structure of two-point function may be useful for computing the thermo-magnetic correction of various quantities associated with a gauge boson.
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We have systematically constructed the general structure of the gauge boson self-energy and the effective propagator in presence of a nontrivial background like hot magnetized material medium. Based on this as well as the general structure of fermion propagator in weakly magnetized medium we have calculated pressure of deconfined QCD matter within HTL approximation.
The one loop self energy of the neutral $rho$ meson is obtained for the effective $rhopipi$ and $rho NN$ 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 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 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 $rho^0$ where one of the modes possesses two fold degeneracy. For large baryonic chemical potential, it is observed that the critical magnetic field required to block the $rho^0rightarrowpi^+pi^-$ decay channel increases significantly with temperature. However, in case of smaller values reaching down to vanishing chemical potential, the critical field follows the opposite trend.
We have evaluated the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor in presence of magnetic field, particularly in a strong field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes effectively (1+1) dimensional strongly correlated system that provides a kinematical threshold based on the mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with increase of the photon energy due to LLL dynamics in a strong field approximation. This strongly enhances the dilepton rate over the thermal perturbative leading order (Born) rate at very low invariant mass. We have also investigated the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong field approximation.
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., ${cal O}[(eB)]$, which causes a marginal improvement over that in the absence of magnetic field.
The electrical and Hall conductivities in a uniform magnetic field are evaluated for an interacting pion gas using the kinetic theory approach within the ambit of relaxation time approximation (RTA). The in-medium cross sections vis-a-vis the relaxation time for $pipi$ scattering are obtained using a one-loop modified thermal propagator for the exchanged $rho$ and $sigma$ mesons using thermal field theoretic techniques. For higher values of the magnetic field, a monotonic increase of the electrical conductivity with the temperature is observed. However, for a given temperature the conductivity is found to decrease steadily with magnetic field. The Hall conductivity, at lower values of the magnetic field, is found to decrease with temperature more rapidly than the electrical conductivity, whereas at higher values of the magnetic field, a linear increase is seen. Use of the in-medium scattering cross-section is found to produce a significant effect on the temperature dependence of both electrical and Hall conductivities compared to the case where vacuum cross-section is used.
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