We derive the relativistic factor for splitting of the $g$-factors of a fermion and its antifermion partner, which is important for placing constraints on dimension-five, $CPT$-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: $|f_e^0|<2.3\times 10^{-12}{\mu }_{\mathrm{B}}$, $|f_p^0|<4\times 10^{-9}{\mu }_{\mathrm{B}}$, and $|f_{\mu }^0|<8\times 10^{-11}{\mu }_{\mathrm{B}}$, respectively, in the laboratory frame (${\mu }_{\mathrm{B}}$ is the Bohr magneton). From existing data, we also extract limits on the coupling strengths of the spatial components, $d^{\perp }$, of related dimension-five interactions of a background field with an electron, proton, neutron, and muon: $|d_e^{\perp }|\lesssim 10^{-9}{\mu }_{\mathrm{B}}$, $|d_p^{\perp }|\lesssim 10^{-9}{\mu }_{\mathrm{B}}$, $|d_n^{\perp }|\lesssim 10^{-10}{\mu }_{\mathrm{B}}$, and $|d_{\mu }^{\perp }|\lesssim 10^{-9}{\mu }_{\mathrm{B}}$, respectively, in the laboratory frame.

• Received 21 July 2014

DOI:https://doi.org/10.1103/PhysRevD.90.045035