Gluon polarization tensor and dispersion relation in a weakly magnetized medium

Abstract

We study the polarization and dispersion properties of gluons moving within a weakly magnetized background at one-loop order. To this end, we show two alternative derivations of the charged fermion propagator in the weak field expansion and use this expression to compute the lowest order magnetic field correction to the gluon polarization tensor. We explicitly show that, in spite of its cumbersome appearance, the gluon polarization tensor is transverse as required by gauge invariance. We also show that none of the three polarization modes develops a magnetic mass and that gluons propagate along the light cone, non withstanding that Lorentz invariance is lost due to the presence of the magnetic field. By comparing with the expression for the gluon polarization tensor valid to all orders in the magnetic field, the existence of a second solution, corresponding to a finite gluon mass, is shown to be spurious and an artifact of the lowest order approximation in the field strength. We also study the strength of the polarization modes for real gluons. We conclude that, provided the spurious solutions are discarded, the lowest order approximation to the gluon polarization and dispersion properties is good as long as the field strength is small compared to the loop fermion mass.

arXiv comment14 pages, 6 figures. Ref.[35] was added

References in corpus (41)

• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• The QCD phase diagram for external magnetic fields
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• QCD quark condensate in external magnetic fields
• Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
• Global polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Inverse magnetic catalysis and the Polyakov loop
• The QCD equation of state in background magnetic fields
• Direct photon production in Pb-Pb collisions at $\sqrt{s_\rm{NN}}$ = 2.76 TeV
• The Importance of Asymptotic Freedom for the Pseudocritical Temperature in Magnetized Quark Matter
• Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC
• Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and Polyakov--Nambu--Jona-Lasinio models
• Conformal anomaly as a source of soft photons in heavy ion collisions
• Inverse magnetic catalysis for the chiral transition induced by thermo-magnetic effects on the coupling constant
• Meson masses in electromagnetic fields with Wilson fermions
• Thermo-magnetic effects in quark matter: Nambu--Jona-Lasinio model constrained by lattice QCD
• Inverse magnetic catalysis in the linear sigma model with quarks
• Azimuthally anisotropic emission of low-momentum direct photons in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV
• Magnetic Field Induced Polarization Difference between Hyperons and Anti-hyperons
• Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels
• The weak-field expansion for processes in a homogeneous background magnetic field
• Dynamical quark mass generation in a strong external magnetic field
• The magnetized effective QCD phase diagram
• Effective potential at finite temperature in a constant magnetic field I: Ring diagrams in a scalar theory
• Inverse magnetic catalysis from the properties of the QCD coupling in a magnetic field
• Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case
• Finite temperature quark-gluon vertex with a magnetic field in the Hard Thermal Loop approximation
• Direct photon elliptic flow in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Thermo-magnetic properties of the strong coupling in the local Nambu--Jona-Lasinio model
• Chiral transition with magnetic fields
• The Magneto-Sono-Luminescence and its signatures in photon and dilepton production in heavy ion collisions
• On the role of magnetic field in photon excess in heavy ion collisions
• General structure of gauge boson propagator and its spectra in a hot magnetized medium
• Prompt photon yield and elliptic flow from gluon fusion induced by magnetic fields in relativistic heavy-ion collisions
• Direct photon production at low transverse momentum in proton-proton collisions at $\sqrt{s}$ = 2.76 and 8 TeV
• Effect of magnetic field on the photon radiation from quark-gluon plasma in heavy ion collisions
• Dissociation of heavy quarkonia in a weak magnetic field
• Low-momentum direct photon measurement in Cu$+$Cu collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV
• Centrality dependence of photon yield and elliptic flow from gluon fusion and splitting induced by magnetic fields in relativistic heavy-ion collisions
• Gluon polarization tensor in a magnetized medium: Analytic approach starting from the sum over Landau levels
• Thermal corrections to the gluon magnetic Debye mass

Cited by in corpus (11)

• Polarization tensor of magnetized quark-gluon plasma at nonzero baryon density
• Anisotropic tomography of heavy quark dissociation by using general propagator structure at finite magnetic field
• Heavy quark dynamics in a strongly magnetized quark-gluon plasma
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• The fermion self-energy and damping rate in a hot magnetized plasma
• Fermion mass and width in QED in a magnetic field
• Catalysis and inverse electric catalysis in a scalar theory
• Thermomagnetic renormalons in a scalar self-interacting $\lambda {\varphi }^4$ theory
• Darker and brighter branes: Suppression and enhancement of photon production in a strongly coupled magnetized plasma
• Strongly interacting matter in extreme magnetic fields
• Interaction field strength between a scalar particle and two massless vector bosons in presence of an external magnetic field