  Aiming at a model-independent analysis of possible new physics effects in
semileptonic processes at various energy scales, we list and study a complete
set of $SU(3)_c\times SU(2)_L\times U(1)_Y$ invariant 4-Fermi operators which
consist of a pair of quarks and a pair of leptons above the electroweak
symmetry breaking. We give a full 1-loop renormalization group treatment of the
evolution of the Wilson coefficients associated with these 4-Fermi operators
between low energy ($\sim$ meson masses) and the cutoff scale $\Lambda$, $\sim
(1-10)$ TeV, where we assume new degree of freedom beyond standard model will
begin to appear and an ultra-violet completion of our effective theory will
take place.
  Motivated by the existing phenomenological bounds, we argue that the new CP
violation can only stem from the scalar and tensor types of 4-Fermi
interaction. Some interesting constraints are obtained by studying the
universality of kaon and pion leptonic decays, CP violating polarization of
$K^+_{\mu 3}$, charged lepton anomalous magnetic moments, and $(\mu\ra e
\gamma)$ like rare decays. In particular, we can use the limit of electron
dipole moment to constrain the size of the CP violating triplet correlation in
the $e^+ e^- \ra t \bar{t}$ process.
