Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

Abstract

We calculate neutral pion mass in presence of an external arbitrary magnetic field in the framework of linear sigma model coupled to quark (LSMq) at zero temperature. We find non-monotonic behavior of pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak field approximation. I. INTRODUCTIONIn heavy-ion collisions (HIC) experiments, a very strong anisotropic magnetic field (∼ 10 19 Gauss) is generated in peripheral collisions due to the relative motion of the colliding ions [1-5] and the direction of the generated magnetic field is perpendicular to the reaction plane. Apart from the HIC, finite magnetic field is also involved in the interior of dense astrophysical objects like compact stars, magnetars [6] and also in the early universe. The effects of such magnetic fields on fundamental particles cannot be neglected and the detailed understanding of the effects on the elementary particles is essential at fundamental levels.One of such effects is the behavior of meson masses as a function of the strength of the magnetic field. The study of magnetic field dependent meson masses is a subject of active research. In Ref.[7], the authors have studied light mesons, namely charged, neutral pions (π ± , π 0 ), rho mesons (ρ ± , ρ 0 ), masses in the presence external electromagnetic field in the framework of lattice quantum chromodynamics (LQCD) and have shown that the magnetic field dependent neutral pion mass decreases with the magnetic field strength.Apart from LQCD calculations, various effective QCD models have been used to study the properties of meson masses in presence of magnetic field. This includes chiralperturbation theory [8,9], pseudoscalar(PS) and pseudovector(PV) pion-nucleon interaction model [10,11], Nambu-Jona Laisino(NJL) model and its extension [12][13][14][15][16], Polyakov loop extension of NJL (PNJL) model [17,18], PQM model [19,20], quark-meson model [21][22][23][24][25].The linear sigma model (LSM) is one of oldest, simplest model in pre-QCD era originally proposed by Gell-Mann and Lévy [26] to describe pion-nucleon interaction. Many global symmetries of QCD is seen to be exhibited * aritra.das@saha.ac.in † nhaque@niser.ac.in

Light pseudo-scalar meson masses under strong magnetic fields within the SU(3) Nambu-Jona-Lasinio model

“…On the other hand, the influence of magnetic fields on the lightest scalar and pseudoscalar mesons (σ and π) has also been calculated mostly using two-flavor schemes, such as chiral perturbation theory [43][44][45][46], the linear sigma model [47][48][49], two-flavor quark-meson model [50], relativistic hamiltonian based formalisms [45,51], effective chiral confinement Lagrangian approach [52,53], QCD sum rules [54], the two-flavor NJL model [34,[55][56][57][58][59][60][61][62][63][64] or its non-local version [65,66]. In this context, there are very few calculations of meson properties incorporating the strange quark.…”

Dimensional reduction and the generalized pion in a magnetic field within the NJL model

“…Unlike thermal QCD systems, the presence of the magnetic field breaks chiral symmetry from SU (2) to U(1), thus, the identified Nambu-Goldstone (NG) boson is reduced from the pseudoscalar triplet to the individual neutral pion [10]. The magnetized masses of neutral and/or charged pions have been calculated by a variety of model approaches, found in [11][12][13][14][15][16][17][18][19][20][21][22].…”

Exposing the effect of $p$-wave in pion triplet under the strong magnetic field

“…Aside from the extensively explored environments at finite temperatures and finite baryon densities, magnetic field arises as a new dimension to analyze the QCD phases and phase transition [6][7][8][9][10]. Motivated by the impact on the evolution of the early universe and the magnetars, where the strength of magnetic field over its surface is up to 10 10 T [11][12][13], and boosted by the novel topological phenomena emerging in off-central heavy-ion collisions [14][15][16], where a stronger eB-field, up to 10 14 − 10 16 T, is produced, the magnetized spectra of pions have been examined in various theoretical approaches for low energy QCD [17][18][19][20][21][22][23][24][25][26][27], within the lattice gauge theory [28] and in the chiral perturbation theory [29][30][31].…”