© World Scientific Publishing Company THE DISPERSIVE APPROACH TO ELECTROWEAK PROCESSES IN THE BACKGROUND MAGNETIC FIELD

We propose a new method to compute amplitudes of electroweak processes in the strong background magnetic field, using 7-+ e+e~ " as an example. We show that the moments of 7 —> • e + e ~ width are proportional to the derivatives of photon polarization function at the zero energy. Hence, the pair-production width can be easily calculated from the latter by the inverse Mellin transform. The prospects of our approach are commented. The electroweak phenomena associated with an intensive background magnetic field are rather rich. Under a background magnetic field, a physical photon can decay into an e+e~ ~ pair or split into two photons. Such processes are relevant to the attenuation of gamma-rays from pulsars1'2. Similarly, with a sufficient energy, a neutrino can go through the decays v — • i/e+e~~3 and u — • 1/74. For processes without charged fermions in the final state, such as 7- » 77 or v-> 1/7, their decay widths can be expressed as asymptotic series in B for B < Bc. However, such asymptotic expansions are not possible for v- * ve+e ~ or 7-> e+e ~ since the wave functions of final-state fermions are non-analytic with respect to the magnetic field strength at B = 0