Tests of CPT and Lorentz symmetry from muon anomalous magnetic dipole moment

TL;DR

This paper derives constraints on CPT-odd and Lorentz-invariance-violating interactions using muon and other fermion g-factor measurements, setting limits on background field couplings from existing experimental data.

Contribution

It provides the first derivation of the relativistic splitting factor for fermion-antifermion g-factors and extracts new limits on background field couplings from experimental data.

Findings

Limits on the temporal component of background fields: |f^0_e|< 2.3×10^{-12} μ_B, |f^0_p|< 4×10^{-9} μ_B, |f^0_μ|< 8×10^{-11} μ_B.

Limits on the spatial components of background fields: |d_e^⊥|, |d_p^⊥|, |d_μ^⊥|, |d_n^⊥| all ≲ 10^{-9} to 10^{-10} μ_B.

Constraints improve understanding of CPT and Lorentz symmetry violations in fundamental physics.

Abstract

We derive the relativistic factor for splitting of the $g$-factors of a fermion and its anti-fermion partner, which is important for placing constraints on dimension-5, $CPT$-odd and Lorentz-invariance-violating interactions from experiments performed in a cyclotron. From existing data, we extract limits (1$\sigma$) on the coupling strengths of the temporal component, $f^0$, of a background field (including the field amplitude), which is responsible for such $g$-factor splitting, with an electron, proton, and muon: $|f^0_e|< 2.3 \times 10^{-12} ~\mu_{\textrm{B}}$, $|f^0_p|< 4 \times 10^{-9} ~\mu_{\textrm{B}}$, and $|f^0_\mu|< 8 \times 10^{-11} ~\mu_{\textrm{B}}$, respectively, in the laboratory frame. From existing data, we also extract limits on the coupling strengths of the spatial components, $d^{\perp}$, of related dimension-5 interactions of a background field with an electron, proton, neutron, and muon: $| {d}_e^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, $| {d}_p^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, $| {d}_n^{\perp} | \lesssim 10^{-10} ~\mu_{\textrm{B}}$, and $| {d}_\mu^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, respectively, in the laboratory frame.