An Effective Operators Analysis of CP Violation : The Semileptonic Case

Abstract

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.