  We calculate for the first time the electric dipole moment (EDM) of the
deuteron, $^3$H, and $^3$He nuclei generated by the one-meson exchange CP-odd
nuclear force in the standard model. The effective $|\Delta S| = 1$ four-quark
operators are matched to the $|\Delta S| = 1$ standard model processes
involving the CP phase of the Cabibbo-Kobayashi-Maskawa matrix at the
electroweak scale and run down to the hadronic scale $\mu = 1$ GeV according to
the renormalization group evolution in the next-to-leading logarithmic order.
At the hadronic scale, the hadron matrix elements are modeled in the
factorization approach. We then obtain the one-meson (pion, eta meson, and
kaon) exchange CP-odd nuclear force, which is the combination of the $|\Delta
S| = 1$ meson-baryon vertices which issue from the penguin operator and the
hyperon-nucleon transition. From this CP-odd nuclear force, the nuclear EDM is
calculated with the realistic Argonne $v18$ interaction and the CP-odd nuclear
force using the Gaussian expansion method. It is found that the EDMs of light
nuclear systems are of order $O(10^{-31}) e $ cm. We also estimate the standard
model contribution to other hadronic CP violating observables such as the EDMs
of $^6$Li, $^9$Be nuclei, and the atomic EDMs of $^{129}$Xe, $^{199}$Hg,
$^{211}$Rn, and $^{225}$Ra generated through the nuclear Schiff moment. We then
analyze the source of theoretical uncertainties and show some possible ways to
overcome them.
