Resonances at the Threshold for Pauli Operators in Dimension Two

It is well-known that, due to the interaction between the spin and the magnetic field, the two-dimensional Pauli operator has an eigenvalue 0 at the threshold of its essential spectrum. We show that when perturbed by an effectively positive perturbation, V, coupled with a small parameter ε, these eigenvalues become resonances. Moreover, we derive explicit expressions for the leading terms of their imaginary parts in the limit ε↘0. These show, in particular, that the dependence of the imaginary part of the resonances on ε is determined by the flux of the magnetic field. The cases of non-degenerate and degenerate zero eigenvalue are treated separately. We also discuss applications of our main results to particles with anomalous magnetic moments.