Pionic dispersion relations in the presence of a weak magnetic field

Abstract

In this work, dispersion relations of ${\pi }^0$ and ${\pi }^{\pm }$ have been studied in vacuum in the limit of weak external magnetic field using a phenomenological pion-nucleon $(\pi N)$ Lagrangian. For our purpose, we have calculated the results up to one loop order in self energy diagrams with the pseudoscalar $(PS)$ and pseudovector $(PV)$ pion-nucleon interactions. By assuming weak external magnetic field it is seen that the effective mass of pion gets explicit magnetic field dependence and it is modified significantly for the case of PS coupling. However, for the PV coupling, only a modest increase in the effective mass is observed. These modified dispersion relations due to the presence of the external field can have substantial influence in the phenomenological aspect of the mesons both in the context of neutron stars as well as relativistic heavy ion collisions.

14 pages, 7 figures (matches published version)

References in corpus (51)

• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Estimate of the magnetic field strength in heavy-ion collisions
• Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
• "Strongly interacting matter in magnetic fields": an overview
• Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in $3+1$ Dimensions
• Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions
• Deconfinement and Chiral Symmetry Restoration in a Strong Magnetic Background
• Chiral transition in a strong magnetic background
• Magnetic fields within color superconducting neutron star cores
• Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field
• Magnetic Color Flavor Locking Phase in High Density QCD
• Color-flavor locked superconductor in a magnetic field
• Color-Superconducting Gap in the Presence of a Magnetic Field
• Color superconducting matter in a magnetic field
• Inverse magnetic catalysis in the linear sigma model with quarks
• The influence of strong magnetic fields and instantons on the phase structure of the two-flavor NJL model
• Phase diagram in an external magnetic field beyond a mean-field approximation
• Quark droplets stability induced by external magnetic field
• Phase diagram of hot magnetized two-flavor color superconducting quark matter
• The weak-field expansion for processes in a homogeneous background magnetic field
• Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma
• Photon decay in strong magnetic field in heavy-ion collisions
• Magnetic Phases in Three-Flavor Color Superconductivity
• Entanglement between chiral and deconfinement transitions under strong uniform magnetic background field
• Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models
• Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields
• The Momentum Dependence of the $\rho -\omega$ Mixing Amplitude in a Hadronic Model
• Thermal pions in a magnetic background
• The magnetized effective QCD phase diagram
• The chiral transition in a magnetic background: Finite density effects and the functional renormalization group
• Chiral transition in a magnetic field and at finite baryon density
• Vacuum structure and chiral symmetry breaking in strong magnetic fields for hot and dense quark matter
• Modification of the B Meson Mass in a Magnetic Field from QCD Sum Rules
• Magnetic contribution to dilepton production in heavy-ion collisions
• Finite temperature quark-gluon vertex with a magnetic field in the Hard Thermal Loop approximation
• On Color Superconductivity in External Magnetic Field
• Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in External Constant Electromagnetic Field
• Chiral transition with magnetic fields
• Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field
• Chiral pions in a magnetic background
• The Linear Sigma Model and the formation of a charged pion condensate in the presence of an external magnetic field
• The Single Flavor Color Superconductivity in a Magnetic Field
• Quark deconfinement and gluon condensate in a weak magnetic field
• Quark matter under strong magnetic field in chiral models
• Off-shell Behavior of the $\pi -\eta$ Mixing Amplitude
• The Delta-Hole model at Finite Temperature
• Symmetry restoration at finite temperature with weak magnetic fields
• Chiral asymmetry in QED matter in a magnetic field
• Chiral asymmetry in cold QED plasma in a strong magnetic field
• Isospin mode splitting and mixing in asymmetric nuclear matter
• Effects of Dirac sea on pion propagation in asymmetric nuclear matter

Cited by in corpus (10)

• Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case
• Meson properties in magnetized quark matter
• Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field
• General structure of fermion two-point function and its spectral representation in a hot magnetised medium
• In medium properties of $K^0$ and $\varphi$ mesons under an external magnetic field
• Hadronic matter under an external magnetic field: in medium modification of the pion mass
• Finite temperature QCD four-point function in the presence of a weak magnetic field within the hard thermal loop approximation
• Neutral pion mass in warm magnetized medium within Linear Sigma Model coupled to Quarks $\left({\text{LSM}}_q\right)$ framework
• ${\rho }^0-\omega$ mixing in the presence of a weak magnetic field
• Pion Mass Modification in presence of external magnetic field