Daniel Gomez Dumm

We analyze the mixing between the π 0 meson and the photon in the presence of a strong uniform magnetic field, in the context of a two-flavor Nambu-Jona-Lasinio model. It is shown that only one specific photon polarization state can get mixed with the π 0 state, a fact that can be understood on general grounds. For magnetic fields with values up to 1 GeV 2 / e , it is found that the effect of the mixing on the pion mass and pion-quark couplings is relatively small (below a level of 15%), which is at variance with previous results reported in the literature.

We study the decays π + → l + ν l in the presence of a background electromagnetic plane wave with circular polarization. We find that, in the presence of this background, the number of hadronic form factors required to describe the pion-to-vacuum amplitude increases from one to four. Three of these form factors are associated with the axial vector current and one with the vector piece, which is in general different from zero. We obtain analytical expressions for the corresponding contributions to the decay width, considering in particular some range of values of interest for the frequency and amplitude of the external wave. For laser frequencies ω of the order of the eV, it is seen that the main correction to the result obtained in absence of the external field is proportional to the vector form factor, carrying a suppression factor of order ∼ ( ω / m π ) 4 / 3 . In addition, we show that our expressions can be connected with the Kroll-Watson formula, which provides the differential cross section for the scattering of a charged particle by some potential in the presence of a strong external electromagnetic wave. Our analytical results are also compatible with previous numerical calculations obtained in the limit of low amplitude laser fields, offering new insight on some characteristics of these results.

We study the anomalous π 0 → γ γ decay under an external uniform magnetic field in the framework of a two-flavor Nambu-Jona-Lasinio model. It is seen that the full decay width gets strongly reduced with the external field, and that the differential width is almost independent of the direction of the outgoing photons. We also find that the result for the total width can be very well approximated by a simple expression obtained at the lowest order in the chiral expansion, which is just a direct extension to finite magnetic fields of the well-known B = 0 result that follows from the anomalous Wess-Zumino-Witten action. As a result, the magnetic suppression of the width can be understood in terms of the evolution of both the neutral pion mass and decay constant with the magnetic field.

We analyze the topological susceptibility and the axion properties in the presence of an external uniform magnetic field, considering a three-flavor Nambu-Jona-Lasinio model that includes strong C P violation through a ’t Hooft-like flavor mixing term. Both thermal and finite density effects are studied for magnetic fields up to 1 GeV 2 , and the corresponding phase transitions are analyzed. To capture the inverse magnetic catalysis effect at finite temperatures and densities, a magnetic-field-dependent coupling constant is considered. Our analytical and numerical results are compared with those previously obtained from lattice QCD, chiral perturbation theory, and other effective models.