  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 $\alpha_{C_T}= \left( 0.520 \pm 0.049
\right) [10^{-20}\, \left<\Sigma\right>_{\text{Xe}}\, e~\text{cm}]$,
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.
