Charged and neutral vectorρmesons in a magnetic field

Abstract

The vector meson ρ in the presence of external magnetic field has been investigated in the framework of the Nambu-Jona-Lasinio model, where mesons are constructed by infinite sum of quark-loop chains by using random phase approximation. The ρ meson polarization function is calculated to the leading order of 1/Nc expansion. It is found that the constituent quark mass increases with magnetic field, the masses of the neutral vector meson ρ 0 with spin component sz = 0, ±1 and the charged vector meson ρ ± with sz = 0 also increases with magnetic field. However, the mass square of the charged vector meson ρ + (ρ − ) with sz = +1 (sz = −1) decreases linearly with magnetic field and drops to zero at the critical magnetic field eBc ≃ 0.2GeV 2 , which indicates the possible condensation of charged vector meson in the vacuum. This critical magnetic field is much lower than the value eBc = 0.6GeV 2 predicted by a point-like vector meson. We also show that if we use lowest Landau level approximation, the mass of the charged vector meson ρ ± for sz = ±1 cannot drop to zero at high magnetic fields.

Electromagnetic fields and anomalous transports in heavy-ion collisions—a pedagogical review

“…possible ρ meson condensation in strong magnetic field [50][51][52][53][54], the neutral pion condensation in vaccum [55], the anisotropic viscosities in hydrodynamic equations [56][57][58][59][60], and the early-stage phenomena in heavy-ion collisions like the EM-field induced particle production [26,[61][62][63][64][65][66] and the dissociation of heavy-flavor mesons [67][68][69][70][71]. These topics will not be the main focus of this article.…”

Determination of the properties of vector mesons in external magnetic field by quenched SU(3) lattice QCD

“…Then the magnetic field was introduced in two flavor lattice QCD simulation [3] and used as the probe of QCD properties [4]. The energies of hadrons in magnetic fields have been calculated on the lattice [5][6][7][8], in theoretical models [9][10][11][12][13] and in the framework of the QCD sum rules [14,15]. The notion of the hadron polarizability was initially JHEP09(2017)142 discussed in [16,17].…”

Survival of charged ρ condensation at high temperature and density

“…[12]. On the other hand, some other results showed that the charged ρ masses indeed decrease with magnetic field and become massless at a critical magnetic field as shown in the NJL model [4,7,8] and in the holographic QCD model [10].…”

“…In Ref. [8], we have obtained the critical magnetic field eB c ≈ 0.2 GeV 2 in the NJL model by calculating the ρ meson polarization function to the leading order of 1/N c expansion.…”

“…Therefore, the Vafa-Witten theorem would not forbid charged ρ meson condensation in an external magnetic field. More studies on charged ρ condensation have been done in different frameworks such as the Nambu-Jona-Lasinio (NJL) model [7,8], lattice QCD [5,9], the gauge/gravity correspondence [10,11], the relativistic Hamiltonian technique [12], and the Dyson-Schwinger equations [13]. On one hand, it was observed that the masses of charged ρ mesons first decrease and then increase with the magnetic field, and cannot drop to zero, as shown by lattice calculations [5], Dyson-Schwinger equations [13] and by solving the meson spectra in a relativistic quark-antiquark system with the relativistic Hamiltonian technique in Ref.…”