By K. Bhattacharya
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Additional info for Elementary Particle Interactions in Bkgd Magnetic Field
For field values larger than this, that particular Landau level does not contribute to the crosssection. To the right of the final spike that appears in the figure, only the zeroth Landau level contributes. In other words, the final electron can go only to the lowest Landau level for such high values of the magnetic field. The exact value of B for which this occurs depends of course on the energy of the initial neutrino. We need to make an important point about these spikes. Each spike in fact go all the way up to infinity.
3) This was calculated using the Schwinger propagator in some very early papers [73, 26]. 4) where εµ , k µ and ω are the polarization vector, the momentum 4-vector and the energy of the initial photon, and the quantity Mℓ was evaluated in various limits by these authors. Fµν is the dual of the electromagnetic field strength tensor. 5) for eB ≫ m2ℓ , where θ is the angle between the photon momentum and the magnetic field. No matter which neutrino pair the photon decays to, both charged leptons appear in the decay rate because of the loop in Fig.
43) In other words, in the standard model 1 cV = − + 2 sin2 θW , 2 1 cA = − . 44) The contribution to b3 from background electrons and positrons was calculated by DNP . 45) where fe and fe are the Fermi distribution functions for electrons and positrons, and E= p2 + m2e . 46) Later authors have improved on this result in two different ways. Some authors  have included the contributions coming from nucleons in the background. Some others [57, 64] have used the Schwinger propagator and extended the results to all orders in the magnetic field.