[Paper Review] A classical picture of lepton neutral current forces

James L. Carr|ArXiv.org|Mar 11, 1999

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper develops a classical field theory analog of the Z-boson neutral current interaction in the Standard Model, deriving Maxwell-like equations for Z-boson fields sourced by electron and neutrino distributions. It computes the neutral current contribution to muonium hyperfine splitting using nonrelativistic perturbation theory, demonstrating parity violation through the field 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.

Motivation & Objective

• To formulate a classical field theory for the neutral current weak interaction, analogous to electromagnetism with a massive photon.
• To derive Maxwell-like equations for Z-boson potentials and fields, treating the Z-boson as a massive vector field.
• To solve these equations for point-like leptons (electrons and neutrinos) and analyze the resulting field structure.
• To apply the classical framework to compute the neutral current contribution to muonium hyperfine structure.
• To explicitly show how parity violation manifests in the classical field solutions.

Proposed method

• Derive Z-boson field equations from the Standard Model Lagrangian, treating the Z-boson as a massive vector field.
• Formulate scalar and vector potentials for the Z-boson, analogous to electromagnetic potentials.
• Define Z-boson electric and magnetic fields as derived from these potentials.
• Solve the field equations for point-like sources representing classical electrons and neutrinos.
• Use nonrelativistic perturbation theory to compute the energy shift in muonium due to Z-exchange.
• Analyze the field solutions to identify explicit parity-violating structures in the interaction.

Experimental results

Research questions

• RQ1 Can a classical field theory be constructed for the neutral current weak interaction, analogous to Maxwell's equations in electromagnetism?
• RQ2 How do the field solutions for Z-boson potentials and fields behave for point-like leptons?
• RQ3 In what way is parity violation encoded in the structure of the classical Z-boson fields?
• RQ4 What is the magnitude of the neutral current contribution to the hyperfine splitting in muonium?
• RQ5 How does the massive nature of the Z-boson affect the classical field behavior and interaction potential?

Key findings

• The Z-boson field equations are derived as a massive vector field theory, formally analogous to electromagnetism with a massive photon.
• The field solutions for point-like electrons and neutrinos exhibit explicit parity-violating structures in their vector and scalar potentials.
• The classical Z-boson fields are shown to mediate a spin-dependent interaction consistent with weak neutral current behavior.
• The neutral current contribution to muonium hyperfine splitting is computed using nonrelativistic perturbation theory.
• The result confirms that the Z-exchange interaction contributes to the hyperfine splitting with a sign and magnitude consistent with parity-violating weak interactions.