In the NJL model, π⁰-γ mixing under strong B fields affects only one polarization state and produces less than 15% change in pion mass and quark couplings up to 1 GeV²/e, at variance with earlier results.
Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
Photons propagating in strong magnetic fields are subject to a phenomenon called the "vacuum birefringence" where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger's proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion-antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.
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$\pi^0$-$\gamma$ mixing in the presence of a strong magnetic field
In the NJL model, π⁰-γ mixing under strong B fields affects only one polarization state and produces less than 15% change in pion mass and quark couplings up to 1 GeV²/e, at variance with earlier results.