Abstract
We investigate both (pseudo)scalar mesons and diquarks in the presence of external magnetic field in the framework of the two-flavored Nambu--Jona-Lasinio (NJL) model, where mesons and diquarks are constructed by infinite sum of quark-loop chains by using random phase approximation. The polarization function of the quark-loop is calculated to the leading order of $1/N_c$ expansion by taking the quark propagator in the Landau level representation. We systematically investigate the masses behaviors of scalar $\sigma$ meson, neutral and charged pions as well as the scalar diquarks, with respect to the magnetic field strength at finite temperature and chemical potential. It is shown that the numerical results of both neutral and charged pions are consistent with the lattice QCD simulations. The mass of the charge neutral pion keeps almost a constant under the magnetic field, which is preserved by the remnant symmetry of QCD$\times$QED in the vacuum. The mass of the charge neutral scalar $\sigma$ is around two times quark mass and increases with the magnetic field due to the magnetic catalysis effect, which is an typical example showing that the polarized internal quark structure cannot be neglected when we consider the meson properties under magnetic field. For the charged particles, the one quark-antiquark loop contribution to the charged $\pi^{\pm}$ increases essentially with the increase of magnetic fields due to the magnetic catalysis of the polarized quarks. However, the one quark-quark loop contribution to the scalar diquark mass is negative comparing with the point-particle result and the loop effect is small.
Highlights
The influence of an external magnetic field on QCD vacuum and matter has attracted great attention in the past few decades, since there are at least three high-energy physical systems where strong magnetic fields may play an important role
NJL model, there is no mechanism for the inverse magnetic catalysis around the critical temperature region, all results in this work are taken below the critical temperature
The one quark-quark loop contribution to the scalar diquark mass is negative and less than 50% of the point-particle result below eB < 0.9 GeV2
Summary
The influence of an external magnetic field on QCD vacuum and matter has attracted great attention in the past few decades (see Refs. [1,2,3]), since there are at least three high-energy physical systems where strong magnetic fields may play an important role. The chiral symmetry breaking and restoration under a strong magnetic field is another significant issue of QCD, which is deeply related to hadrons’ properties, such as the pion mass and the pion decay constant via the Gell-Mann-Oakes-Renner (GOR) relation [69]. It means that, exploring the modification of hadrons’ properties in the magnetized hot and/or dense medium, will help to understand the effects of magnetic fields on the chiral phase transition at finite temperature and chemical potential.
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