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Measuring the size of permanent electric dipole moments (EDM) of a particleor system provides a powerful tool to test Beyond-the-Standard-Model physics.The diamagnetic $^{129}$Xe atom is one of the promising candidates for EDMexperiments due to its obtainable high nuclear polarization and its longspin-coherence time in a homogeneous magnetic field. By measuring the spinprecession frequencies of polarized $^{129}$Xe and $^{3}$He, a new upper limiton the $^{129}$Xe atomic EDM $d_\mathrm{A}(^{129}\mathrm{Xe})$ was reported inPhys. Rev. Lett. 123, 143003 (2019). This writeup proposes a new evaluationmethod based on global phase fitting (GPF) for analyzing the continuous phasedevelopment of the $^{3}$He-$^{129}$Xe comagnetometer signal. The Cramer-RaoLower Bound on the $^{129}$Xe EDM for the GPF method is theoretically derivedand shows the benefit of achieving high statistical sensitivity withoutbringing new systematic uncertainties. The robustness of the GPF method isverified with Monte-Carlo studies. By optimizing the analysis parameters andadding few more data that could not be analyzed with the former method, aresult of \[ { d_\mathrm{A} (^{129}\mathrm{Xe})=(1.1 \pm 3.6_\mathrm{(stat)}\pm 2.0_\mathrm{(syst)})\times 10 ^{-28} e~\mathrm{cm}}, \] is obtained and isused to derive the upper limit of $^{129}$Xe permanent EDM at 95\% C.L. \[{|d_\text{A}(^{129}\text{Xe})| < 8.3 \times 10^{-28}~e~\mathrm{cm}}. \] Thislimit is a factor of 1.7 smaller as compared to the previous result.

A global phase fitting approach for the analysis of $^{129}$Xe electric dipole moment measurements