The pole and screening masses of neutral pion in hot and magnetized medium: a comprehensive study in the Nambu--Jona-Lasinio model

Abstract

In this work, we investigate not only the pole masses but also the screening masses of neutral pions at finite temperature and magnetic field by utilizing the random phase approximation (RPA) approach in the framework of the two-flavor Nambu--Jona-Lasinio (NJL) model. And two equivalent formalisms in the presence of a magnetic field, i.e. the Landau level representation (LLR) and the proper-time representation (PTR), are applied to obtain the corresponding analytical expressions of the polarization functions (except the expressions for the pole masses in the PTR). In order to evaluate the applicable region of the low-momentum expansion (LME), we compare the numerical results within the full RPA (FRPA) with those within the reduced RPA (RRPA), i.e. the RPA in the LME. It is confirmed that the pole masses of π0in the FRPA suffer a sudden mass jump at the Mott transition temperature when in the presence of external magnetic field, and the Mott transition temperature is catalyzed by the magnetic field. And by analyzing the behaviors of the directional sound velocities of π0, which are associated with the breaking of the Lorentz invariance by the heat bath and the magnetic field, we clarify the two problems existing in previous literatures: one is that the transverse sound velocities in the medium are always larger than unity and thus violate the law of causality on account of the non-covariant regularization scheme, the other is that the longitudinal sound velocities are identically equal unity at finite temperature on account of the limitation of the derivative expansion method used.

References in corpus (27)

• The Chiral Magnetic Effect
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Charge separation induced by P-odd bubbles in QCD matter
• Testing the chiral magnetic and chiral vortical effects in heavy ion collisions
• Superconductivity of QCD vacuum in strong magnetic field
• The Importance of Asymptotic Freedom for the Pseudocritical Temperature in Magnetized Quark Matter
• Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and Polyakov--Nambu--Jona-Lasinio models
• Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model
• The melting of charmonium in a magnetic field from an effective AdS/QCD model
• Charmonium Spectroscopy in Strong Magnetic Fields by QCD Sum Rules: S-Wave Ground States
• Charged and neutral vector meson under magnetic field
• Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model
• QCD sum rules for magnetically induced mixing between ${\eta }_c$ and $J/\psi$
• Effect of anomalous magnetic moment of quarks on the phase structure and mesonic properties in the NJL model
• Magnetized baryons and the QCD phase diagram: NJL model meets the lattice
• Dynamical polarization of monolayer graphene in a magnetic field
• Heavy meson spectroscopy under strong magnetic field
• Neutral and charged pion properties under strong magnetic fields in the NJL model
• Spectral properties of $\rho$ meson in a magnetic field
• Hadrons in Strong Electric and Magnetic Fields
• Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field
• Charmonium decay widths in magnetized matter
• Octet Baryons in Large Magnetic Fields
• Modification of the masses of the lightest neutral mesons in a hadronic medium under an external magnetic field
• Neutron in a Strong Magnetic Field: Finite Volume Effects
• Skyrme model study of proton and neutron properties in a strong magnetic field
• Nucleon and $\Delta$ isobar in a strong magnetic field

Cited by in corpus (21)

• Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium
• Pion dynamics in a soft-wall AdS-QCD model
• Impacts of (inverse) magnetic catalysis on screening masses of neutral pions and sigma mesons in hot and magnetized quark matter
• Thermal properties of light mesons from holography
• Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis
• Mass spectra of neutral mesons $K_0,{\pi }_0,\eta ,{\eta }^{\prime }$ at finite magnetic field, temperature and baryon chemical potential
• Quark anomalous magnetic moment leads to the inverse magnetic catalysis phenomena of chiral restoration and deconfinement phase transitions in ${\mu }_B-T$ plane
• Causality violation and the speed of sound of hot and dense quark matter in the Nambu--Jona-Lasinio model
• Magnetic catalysis and diamagnetism from pion fluctuations
• Do we need to use regularization on the thermal part in the NJL model?
• Functional renormalization group study of neutral and charged pion under magnetic fields in the quark-meson model
• Magnetic field dependence of the neutral pion longitudinal screening mass in the linear sigma model with quarks
• Chiral symmetry restoration and properties of Goldstone bosons at finite temperature
• Exposing the effect of $p$-wave in pion triplet under the strong magnetic field
• Strongly interacting matter in extreme magnetic fields
• Thermomagnetic effects on light pseudo-scalar meson masses within the SU(3) Nambu-Jona--Lasinio model
• QCD chiral condensate and pseudoscalar-meson properties in the nuclear medium at finite temperature
• Dimensional reduction and the generalized pion in a magnetic field within the NJL model
• Spectral function for pions in magnetic field
• Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model
• Light mesons around critical end points in $T-{\mu }_B-{\mu }_I-eB$ space