New perspective for the magnetic corrections to π-π scattering lengths in the linear sigma model

Abstract

In this article, a new perspective for obtaining the magnetic evolution of π-π scattering lengths in the linear sigma model is presented. When computing the relevant one-loop diagrams that contribute to these parameters, the sum over Landau levels—emerging from the expansion of the Schwinger propagator–is handled in a novel way that could also be applied to the calculation of other magnetic-type corrections. Essentially, we obtain an expansion in terms of Hurwitz zeta functions. It is necessary to regularize our expressions by an appropriate physical subtraction when jqBj → 0 (where q is the meson charge and B is the magnetic field strength). In this way, we are able to interpolate between the very high-magnetic-fieldstrength region (usually handled in terms of the lowest Landau level approximation) and the weak-field region (discussed in a previous paper by some of us), which is based on an appropriate expansion of the Schwinger propagator up to order jqBj2. Our results for the scattering length parameters produce a soft evolution for a wide range of magnetic field strengths, reducing to the previously found expressions in both limits.