A classical picture of lepton neutral current forces

TL;DR

This paper develops a classical electromagnetic analogy for Z-boson neutral current forces, deriving Maxwell-like equations from the standard model and applying them to compute effects on muonium hyperfine structure.

Contribution

It introduces a classical field framework for neutral current weak interactions, deriving Maxwell-like equations for the Z-boson and applying them to specific atomic phenomena.

Findings

Derived Maxwell equations for Z-boson fields from the standard model

Solved for point sources representing electrons and neutrinos

Calculated neutral current effects on muonium hyperfine structure

Abstract

When charged current weak interations are excluded, the neutral current weak interaction is formally similar to ordinary electromagnetism with a massive photon. In this spirit, the Maxwell equations for the fields of the Z-boson are derived from the standard model. These describe the Z-boson scalar and vector potentials, and the Z-boson electric and magnetic fields whose sources are electron and neutrino distributions and currents. The Z-boson Maxwell equations are solved for point sources representing classical point-like electrons and neutrinos. The parity violation of the weak interation is manifest in the structure of these solutions. As an application of this model, the neutral current contribution to the muonium hyperfine structure is computed using nonrelativistic perturbation theory.