A new look at the pair-production width in a strong magnetic field

We reexamine the process γ→e++e− in a background magnetic field comparable to Bc≡me2/e. This process is known to be non-perturbative in the magnetic-field strength. However, it can be shown that the moments of the above pair production width are proportional to the derivatives of photon polarization function at the zero energy, which is perturbative in B. Hence, the pair-production width can be easily obtained from the latter by the inverse Mellin transform. The implications of our approach are discussed.