We report the results of our theoretical studies of the time-reversal and parity violating electric dipole moment (EDM) of 129 Xe arising from the nuclear Schiff moment (NSM) and the electronnucleus tensor-pseudotensor (T-PT) interaction based on the self-consistent and the normal relativistic coupled-cluster methods. The important many-body effects are highlighted and their contributions are explicitly presented. The uncertainties in the calculations of the correlation and relativistic effects are determined by estimating the contributions of the triples excitations, and the Breit interaction respectively, which together amount to about 0.7% for the NSM and 0.2% for the T-PT interactions. The results of our present work in combination with improved experimental limits for 129 Xe EDM in the future would tighten the constraints on the hadronic CP violating quantities, and this could provide important insights into new physics beyond the Standard Model of elementary particles.The observation of the electric dipole moment (EDM) of a non degenerate system would be a signature of violations of both time-reversal (T) and parity (P) symmetries [1,2]. The CPT theorem implies that T violation amounts to CP violation [3]. The Standard Model (SM) of particle physics contains CP violation in the form of a complex phase in the Kobayashi-Maskawa matrix, which however cannot explain the large matterantimatter asymmetry observed in the Universe [4]. This suggests [5,6] that although the SM predicts very small values for atomic EDMs, their actual sizes could lie close to the current experimental limits [7].The EDMs of diamagnetic atoms have the potential to probe new physics at energy scales much higher than TeV [8]. They are primarily sensitive to the nuclear Schiff Moment (NSM) and the tensor-pseudotensor (T-PT) electron-nucleus interaction [8]. The former arises due to CP violating nucleon-nucleon interactions and the EDMs of nucleons, which at the level of elementary particles arise from CP violating quark-quark interactions and the EDMs and chromo-EDMs of quarks [8]. On the other hand, the latter is due to the T-PT electron-nucleon interaction originating from the T-PT electron-quark interaction, which has been predicted by leptoquark models [9].There have been important developments in the search for EDMs of elementary particles and composite systems in recent years. The most stringent EDM limit to date, d Hg < 7.4 × 10 −30 e · cm (95% confidence level (C.L.)), comes from the diamagnetic atom, 199 Hg [10]. This unprecedented precision has been achieved due to the steady improvements in the spin precession measurement for this atom over the past three decades. The first result for another diamagnetic atom, 225 Ra, for which the nuclear octupole deformation is expected to amplify its atomic EDM by about two -to three orders of mag-nitude [11], was reported 3 years ago [12] to be d Ra < 1.4×10 −23 e·cm (95% C.L.). As for the 129 Xe diamagnetic atom, three experiments on its EDM are currently under way [13][14][15]. Among the ...