Pion-to-vacuum vector and axial vector amplitudes and weak decays of pions in a magnetic field

Understand

We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field.

• It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors.
• Within this framework we obtain a general expression for the weak decay $\pi^- \to l\,\bar\nu_l$ and discuss the corresponding limits of strong and weak external magnetic fields.