It is simply anticipated that in a strong magnetic configuration, the Landau quantization ceases the neutral rho meson to decay to the charged pion pair, so the neutral rho meson will be long-lived. To closely access this naive observation, we explicitly compute the charged pion-loop in the magnetic field at the one-loop level, to evaluate the magnetic dependence of the lifetime for the neutral rho meson as well as its mass. Due to the dimensional reduction induced by the magnetic field (violation of the Lorentz invariance), the polarization (spin sz = 0, ±1) modes of the rho meson, as well as the corresponding pole mass and width, are decomposed in a nontrivial manner compared to the vacuum case. To see the significance of the reduction effect, we simply take the lowest-Landau level approximation to analyze the spin-dependent rho masses and widths. We find that the "fate" of the rho meson may be more complicated because of the magnetic-dimensional reduction: as the magnetic field increases, the rho width for the spin sz = 0 starts to develop, reach a peak, to be vanishing at the critical magnetic field to which the folklore refers. On the other side, the decay rates of the other rhos for sz = ±1 monotonically increase as the magnetic field develops. The correlation between the polarization dependence and the Landau-level truncation is also addressed.

We explore magnetic field effects on the nuclear matter based on the skrymion crystal approach for the first time. It is found that the magnetic effect plays the role of a catalyzer for the topological phase transition (topological deformation for the skyrmion crystal configuration from the skrymion phase to half-skyrmion phase). Furthermore, we observe that in the presence of the magnetic field, the inhomogeneous chiral condensate persists both in the skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic field gets larger, the inhomogeneous chiral condensate in the skyrmion phase tends to be drastically localized, while in the half-skyrmion phase the inhomogeneity configuration is hardly affected. It also turns out that a large magnetic effect in a low density region distorts the baryon shape to an elliptic form but the crystal structure is intact. However, in a high density region, the crystal structure is strongly effected by the strong magnetic field. A possible correlation between the chiral inhomogeneity and the deformation of the skrymion configuration is also addressed. The results obtained in this paper might be realized in the deep interior of compact stars.

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We discuss the magnetic responses of vector meson masses based on the hidden local symmetry (HLS) model in constant magnetic field, described by the lightest two-flavor system including the pion, rho and omega mesons in the spectrum. The effective masses influenced under the magnetic field are evaluated in a way of the derivative/chiral expansion established in the HLS model. At the leading order O(p 2 ) the g-factor of the charged rho meson is fixed to be 2, implying that the rho meson at this order is treated just like a point-like spin-1 particle. Beyond the leading order, one finds anomalous magnetic interactions of the charged rho meson, involving the anomalous magnetic moment, which give corrections to the effective mass. It is then suggested that up to O(p 4 ) the charged rho meson tends to become massless. Of interest is that nontrivial magnetic-dependence of neutral mesons emerges to give rise to the significant mixing among neutral mesons. Consequently, it leads to the dramatic enhancement of the omega meson mass, which is testable in future lattice simulations. Corrections from terms beyond O(p 4 ) are also addressed.

It is expected that in a hot QCD system, a local parity-odd domain can be produced due to nonzero chirality, which is induced from the difference of winding numbers carried by the gluon topological configuration (QCD sphaleron). This local domain is called the chiral-imbalance medium characterized by nonzero chiral chemical potential, which can be interpreted as the time variation of the strong CP phase. We find that the chiral chemical potential generates the parity breaking term in the electromagnetic form factor of charged pions. Heavy ion collision experiments could observe the phenomenological consequence of this parity-odd form factor through the elastic scattering of a pion and a photon in the medium. Then we quantify the asymmetry rate of the parity violation by measuring the polarization of the photon associated with the pion, and discuss how it could be measured in a definite laboratory frame. We roughly estimate the typical size of the asymmetry, just by picking up the pion resonant process, and find that the signal can be sufficiently larger than possible background events from parity-breaking electroweak process. Our findings might provide a novel possibility to make a manifest detection for the remnant of the strong CP violation.