Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model

Abstract

In this review, we summarize recent progresses on the possible phases of quantum chromodynamics (QCD) in the presence of a strong magnetic field, mainly from the views of chiral effective Nambu-Jona-Lasinio model. Four kinds of phase transitions are explored in detail: chiral symmetry breaking and restoration, neutral pseudoscalar superfluidity, charged pion superfluidity and charged rho superconductivity. In particular, we revisit the unsolved problems of inverse magnetic catalysis effect and the competition between chiral density wave and solitonic modulation, and eventually manage to obtain useful results by adopting self-consistent schemes.

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

“…Note that the 't Hooft-Maekawa interaction together with the uniform magnetic field B induce a mix of neutral mesons states with equal flavors, i.e. π 0 , η, η ′ [72]. We see that, except for η ′ , neutral pseudoscalar mesons display a non-monotonous behavior when using a constant coupling, which shifts to a monotonous decrease in concordance with LCQD results when a magnetic coupling is introduced.…”

“…II, at the quadratic level the inverse propagators corresponding to the neutral π 3 , η 0 and η 8 fields are arranged in terms of a symmetric 3x3 matrix; the pole-masses and widths of the physical mesons (π 0 , η and η ′ ) are obtained as the roots of this inverse propagator matrix determinant. Note that in the B = 0 case, besides the 't Hooft-Maekawa interaction which breaks the U A (1) symmetry and is responsible for the coupling between the η 0 and η 8 , the magnetic field also breaks the isospin symmetry, leading to a mixing between all three states [72]. This is in contrast to the B = 0 case where due to the isospin symmetry (M u = M d ) the π 3 field is decoupled leaving only η 0 and η 8 mixed in a symmetric 2x2 matrix.…”

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

“…Usually, global properties of low energies hadrons can be suitably investigated by means of hadron effective models and effective field theories whose use have been extended, more recently, for hadrons in strong magnetic fields [15,1,18,19,20,21,22]. Among the successful QCD effective models, the Nambu-Jona-Lasinio (NJL) model is known to reproduce, and eventually to predict, many observables for the hadron structure and dynamics under different conditions [23,24,25,26,19].…”

Inverse magneto-rotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

“…These effects, including the (inverse) magnetic catalysis (see [10] and the references therein) and the chiral magnetic effect [11], are the subject of intensive studies in recent years. In particular, the impact of a constant magnetic field on the QCD phase diagram is studied intensively in the literature [7,12]. The main focus here is on the catalytic effect of constant magnetic fields.…”

“…This effect, which is previously dubbed "inverse magnetic catalysis" [17], is shown to be present in dense quark matter [7], or once the anomalous magnetic moment of the quark matter is nonzero [18], or an axial vector interaction is present [19], or when the scalar coupling constant of effective models depends on the magnetic field [20,21], or for nonlocal chiral quark models, [22]. The true reason for the inverse magnetic catalysis is still under debate (see [12] and the references therein).…”