  In this article, a new perspective for obtaining the magnetic evolution of
$\pi-\pi $ scattering lengths in the frame of 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 have
obtained an expansion in terms of Hurwitz Zeta functions. It is necessary to
regularize our expressions by an appropriate physical subtraction when $|qB|
\rightarrow 0$ ($q$ the meson charge and $B$ the magnetic field strength). In
this way, we are able to interpolate between the very high magnetic field
strength region, usually handled in terms of the Lowest Landau Level (LLA)
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 $|qB|^{2}$. Our results for the scattering lengths parameters
produce a soft evolution in a wide region of magnetic field strengths, reducing
to the previously found expressions in both limits.
