Muon Interactions with Fermionic Currents in Quantum Chromodynamics: A Theoretical Review of Hadronic Contributions and Lattice QCD Approaches

Abstract

Muon observables provide one of the most stringent precision tests of the Standard Model. Although the muon is a lepton and therefore does not directly participate in Quantum Chromodynamics (QCD), strong-interaction effects enter through hadronic vacuum polarization and hadronic light-by-light scattering. These non-perturbative QCD contributions dominate the theoretical uncertainty in the muon anomalous magnetic moment (g−2). This review summarizes the role of fermionic quark currents in QCD, the emergence of hadronic corrections, lattice QCD methodologies, and recent theoretical developments. Particular emphasis is placed on how quark-gluon dynamics influence precision muon measurements and constrain possible physics beyond the Standard Model. 

Keywords: Quantum Chromodynamics, Muon, Fermions, Hadronic Vacuum Polarization, Lattice QCD, Standard Model, Muon g−2

1. Introduction

Quantum Chromodynamics is the SU(3) gauge theory describing interactions among quarks and gluons. Quarks are spin-½ fermions carrying colour charge, while gluons are the gauge bosons responsible for the strong interaction.

Although the muon is colour neutral, virtual hadronic processes generated by quark-antiquark pairs significantly modify electromagnetic interactions involving muons. Precision measurements of the muon anomalous magnetic moment therefore provide a sensitive probe of QCD dynamics. 

4. Lattice QCD Methods

Lattice QCD discretizes space-time into a finite grid and evaluates the QCD path integral numerically.

Advantages include:

first-principles calculations,

non-perturbative treatment,

systematic improvement with increasing lattice resolution.

Recent lattice calculations have substantially improved predictions of hadronic contributions to the muon magnetic moment. 

5. Discussion

Current theoretical challenges include:

reducing uncertainties in hadronic vacuum polarization,

improving lattice precision,

reconciling different theoretical determinations,

testing for possible beyond-Standard-Model effects.

Future facilities and computational advances are expected to refine these predictions further. 

6. Conclusion

The interplay between muons and QCD is indirect but fundamental. Fermionic quark currents generate hadronic effects that dominate uncertainties in precision muon observables. Continued progress in lattice QCD and precision experiments will improve Standard Model tests and may reveal evidence of new physics.

References

1. T. Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model, Physics Reports (2020). 

2. C. Lehner, High-precision lattice QCD calculations of the muon anomalous magnetic moment, Nature Reviews Physics (2022). 

3. T. Blum, M. Hayakawa, T. Izubuchi, Hadronic corrections to the muon anomalous magnetic moment from lattice QCD. 

4. E. Estrada, A. Miranda, P. Roig, Hadronic contributions to the muon anomalous magnetic moment within resonance chiral theory (2026).