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 (20)

• Chiral transition in a strong magnetic background
• 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
• 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
• The magnetized effective QCD phase diagram
• The chiral transition in a magnetic background: Finite density effects and the functional renormalization group
• Vacuum structure and chiral symmetry breaking in strong magnetic fields for hot and dense quark matter
• Finite temperature quark-gluon vertex with a magnetic field in the Hard Thermal Loop approximation
• Chiral transition with magnetic fields
• Quark matter under strong magnetic field in chiral models
• Quark deconfinement and gluon condensate in a weak magnetic field
• Symmetry restoration at finite temperature with weak magnetic fields
• 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