Abstract
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 ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}l{\overline{\ensuremath{\nu}}}_{l}$ and discuss the corresponding limits of strong and weak external magnetic fields.
Highlights
The effect of intense magnetic fields on the properties of strongly interacting matter has gained significant interest in recent years [1,2,3]
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
In this work we present a general method to parametrize the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform static magnetic field B⃗
Summary
The effect of intense magnetic fields on the properties of strongly interacting matter has gained significant interest in recent years [1,2,3]. In that work it is noted that the existence of the background field opens the possibility of a nonzero pion-to-vacuum transition via the vector piece of the electroweak current, which implies the existence of a further decay constant Taking into account this new constant, the authors of Ref. Considering an external uniform magnetic field, we determine the form of the most general model-independent hadronic matrix elements, written in terms of gauge covariant Lorentz structures. Given the general form of the hadronic matrix elements, we obtain an expression for the π− → lνl decay width, taking into account the effect of the magnetic field on both pion and lepton wave functions. We include Appendixes A, B, C and D to quote technical details of our calculations
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