Past Electron-Positron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">g</mml:mi><mml:mi>−</mml:mi><mml:mn>2</mml:mn></mml:math>Experiments Yielded Sharpest Bound on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">CPT</mml:mi></mml:math>Violation for Point Particles

In our experiments on a single ${e}^{\ensuremath{-}}$ and ${e}^{+}$ we measured the cyclotron and spin-cyclotron difference frequencies ${\ensuremath{\omega}}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\ensuremath{\omega}}_{a}^{\ifmmode\pm\else\textpm\fi{}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\omega}}_{s}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}{\ensuremath{\omega}}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ and ratios ${a}^{\ifmmode\pm\else\textpm\fi{}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\omega}}_{a}^{\ifmmode\pm\else\textpm\fi{}}/{\ensuremath{\omega}}_{c}^{\ifmmode\pm\else\textpm\fi{}}$ at ${\ensuremath{\omega}}_{c}/2\ensuremath{\pi}\ensuremath{\simeq}141\mathrm{GHz}$ and ${e}^{\ensuremath{-}}$ values also at ${\ensuremath{\omega}}_{c}/2\ensuremath{\pi}\ensuremath{\simeq}164\mathrm{GHz}$. Here we do extract from these data a new figure of merit for violation of $\mathrm{CPT}$ symmetry similar to $|{m}_{\mathrm{Kaon}}{\ensuremath{-}m}_{\mathrm{Antikaon}}|{/m}_{\mathrm{Kaon}}\ensuremath{\lesssim}{10}^{\ensuremath{-}18}$ for the $K$ mesons composed of two quarks. That expression compares experimental relativistic mass energies of particle states before and after the $C,P,T$ operations have transformed particle into antiparticle. The figure for our noncomposite leptons was even smaller: $|\ensuremath{\Elzxh}({\ensuremath{\omega}}_{a}^{\ensuremath{-}}/2)\ensuremath{-}\ensuremath{\Elzxh}({\ensuremath{\omega}}_{a}^{+}/2)|{/m}_{0}{c}^{2}\ensuremath{\lesssim}12\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$.