Effective-Lagrangian approach to precision measurements: the anomalous magnetic moment of the muon

TL;DR

The work develops an effective Lagrangian framework to study how beyond-Standard-Model physics can affect the muon anomalous magnetic moment $a_\mu$, distinguishing decoupling and non-decoupling regimes. It introduces gauge-invariant dimension-six operators and, in the non-decoupling case, a chiral Lagrangian with additional beta-parameters, to categorize contributions to $a_\mu$ into loop-induced, gauge-eigenstate modification, and direct dipole terms. The analysis finds that indirect effects in the decoupling scenario are typically too small to probe high scales, while direct dipole terms can, in principle, reach sensitivity to $\Lambda$ of tens of TeV (depending on suppression factors). In the non-decoupling case, direct terms may be observable if not heavily suppressed by $m_\mu/\Lambda$, and Brookhaven-like experiments could either detect such effects or impose meaningful limits, though assumptions about underlying dynamics and couplings remain crucial. Overall, the paper clarifies how precision $a_\mu$ measurements constrain high-energy physics through an operator-based, gauge-invariant EFT approach, highlighting the role of RG running and the distinct signatures of decoupling versus non-decoupling new physics.

Abstract

We investigate the use of effective Lagrangians to describe the effects on high-precision observables of physics beyond the Standard Model. Using the anomalous magnetic moment of the muon as an example, we detail the use of effective vertices in loop calculations. We then provide estimates of the sensitivity of new experiments measuring the muon's $ g - 2 $ to the scale of physics underlying the Standard Model.