We calculate interaction constants for the contributions from PT-odd scalar-pseudoscalar and tensor-pseudotensor operators to the electric dipole moment of ${}^{129}$Xe, for the first time in case of the former, using relativistic many-body theory including the effects of dynamical electron correlations. These interaction constants are necessary ingredients to relating the corresponding measurements to fundamental parameters in models of physics beyond the Standard Model. We obtain $alpha_{C_S} = left( 0.71 pm 0.18 right) [10^{-23}, e~text{cm}]$ and $alpha_{C_T}= left( 0.520 pm 0.049 right) [10^{-20}, left<Sigmaright>_{text{Xe}}, e~text{cm}]$, respectively. We apply our results to test a phenomenological relation between the two quantities, commonly used in the literature, and discuss their present and future phenomenological impact.
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