# Equations of motion, symmetry currents and EFT below the electroweak scale

## TL;DR

This paper derives the equations of motion and symmetry currents for the low-energy effective field theory below the electroweak scale, incorporating higher dimensional operators and analyzing their impact on conserved currents and gauge interactions.

## Contribution

It provides a detailed construction of equations of motion and symmetry currents in the EFT below the electroweak scale, including effects of operators up to dimension six.

## Key findings

- Higher dimensional operators modify equations of motion and conserved currents.
- Surface terms relate to multipole charge distributions sourcing gauge fields.
- Electromagnetic current corrections reflect multipole contributions.

## Abstract

The low-energy effective field theory is constructed by integrating out Standard Model states with masses proximate to the electroweak scale. We report the equations of motion for this theory, including corrections due to higher dimensional operators up to mass dimension six. We construct the corresponding symmetry currents, and discuss how the $\rm SU(2)_L \times U(1)_{\mathsf{y}}$ symmetry, and global symmetries, are manifested when Standard Model states are integrated out. Including contributions from higher dimensional operators to the equations of motion modifies the interpretation of conserved currents. We discuss the corrections to the electromagnetic current as an example, showing how modifications to the equation of motion, and corresponding surface terms, have a direct interpretation in terms of multipole charge distributions that act to source gauge fields.