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Beyond QED: Electroweak and hadronic extensions of McMule

Sophie Kollatzsch

Abstract

McMule is a Monte Carlo framework developed to advance the low-energy precision frontier by providing QED corrections to leptonic scattering and decay processes, currently up to next-to-next-to-leading order. Recent developments have extended its capabilities in two important directions: the systematic inclusion of electroweak effects at low energies within the low-energy effective field theory [arXiv:2507.17652], and the incorporation of pion form factors and the non-perturbative hadronic vacuum polarisation in loop amplitudes through a combination of OpenLoops and effective field theory techniques, referred to as disperon QED [arXiv:2512.10709]. I will provide an overview of McMule and discuss these recent extensions and their applications. In particular, I will illustrate the impact of the model used for non-perturbative $γ$-$Z$ mixing effects in the context of the MOLLER experiment and highlight the subtlety involved in consistently aligning OpenLoops with its effective field theory expansion in disperon QED.

Beyond QED: Electroweak and hadronic extensions of McMule

Abstract

McMule is a Monte Carlo framework developed to advance the low-energy precision frontier by providing QED corrections to leptonic scattering and decay processes, currently up to next-to-next-to-leading order. Recent developments have extended its capabilities in two important directions: the systematic inclusion of electroweak effects at low energies within the low-energy effective field theory [arXiv:2507.17652], and the incorporation of pion form factors and the non-perturbative hadronic vacuum polarisation in loop amplitudes through a combination of OpenLoops and effective field theory techniques, referred to as disperon QED [arXiv:2512.10709]. I will provide an overview of McMule and discuss these recent extensions and their applications. In particular, I will illustrate the impact of the model used for non-perturbative - mixing effects in the context of the MOLLER experiment and highlight the subtlety involved in consistently aligning OpenLoops with its effective field theory expansion in disperon QED.
Paper Structure (6 sections, 7 equations, 2 figures)

This paper contains 6 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Overview of McMule
  3. Recent developments
  4. Bringing hadrons into the loop
  5. Adding electroweak effects
  6. Plans for the future

Figures (2)

  • Figure 1: Example contributions and hadronic data input for $ee\to\pi\pi$.
  • Figure 3: $A_{LR}$ for the MOLLER experiment as a function of $\theta$ defined in \ref{['eq:CoMtheta']} for three choices of $\mu_s$ in RGE-improved perturbation theory. The bottom panel shows the impact of using a different model for the hadronic $\Pi_{\gamma 3}$ as defined in \ref{['eq:HVPimpact']}.