  We perform a systematic study of flavor-diagonal parity- and
time-reversal-violating operators of dimension six which could arise from
physics beyond the SM. We begin at the unknown high-energy scale where these
operators originate. At this scale the operators are constrained by gauge
invariance which has important consequences for the form of effective operators
at lower energies. In particular for the four-quark operators. We calculate
one-loop QCD and, when necessary, electroweak corrections to the operators and
evolve them down to the electroweak scale and subsequently to hadronic scales.
We find that for most operators QCD corrections are not particularly
significant. We derive a set of operators at low energy which is expected to
dominate hadronic and nuclear EDMs due to physics beyond the SM and obtain
quantitative relations between these operators and the original dimension-six
operators at the high-energy scale. We use the limit on the neutron EDM to set
bounds on the dimension-six operators.
