Higgs Physics and Cp Violation

The CP violation in K and B decays are discussed with the emphasize on the precise prediction for ǫ ′ /ǫ and the new physics effects from a class of models with additional Higgs doublets and fermions. The contributions from standard model with two-Higgs-doublet (S2HDM) to K, B mixing and decays are briefly reviewed. The possible large effects on CP violation in B → φK is discussed in an extended standard model with both an additional Higgs doublet and fourth generation quarks (S2HDM4). We show that although the S2HDM and the Standard model with fourth generation quarks alone are not likely to largely change the effective sin 2β from the decay of B → φK S , the S2HDM4 model can easily account for the possible large deviation of sin 2β without conflicting with other experimental constraints. The origin of CP violation with the SM and beyond is currently under intense investigation. In this talk we will focus on the CP violations in hadronic K and B meson decays. The decays K → ππ are described by a low energy effective Hamiltonian with short and long distrance contributions obsorbed into Wilson coefficients and matrix elements of local operators respectively. Matrix elements for two of these operators, Q 6 and Q 8 , are most important for the evaluation of direct CP violation parameter ε ′ /ε. The Wil-son coefficients depend on scal µ and to next-to-leading order (NLO) corrections in a more complicated way which depends also on the renormalization scheme. The main issue is the evaluation of long distance contributions. It was the first time pointed out in Ref. 1 that with long distance chiral-loop corrections to operator Q 6 , ε ′ /ε could reach O(10 −3). For a consistent description to K → ππ, one needs a matching between short and long distance terms. In the naive matching approaches 2 with the cutoff scale of M for matrix element being identified with short distance scale µ at about 1 GeV, a large correction originates from rescattering of the pions, i.e., K → ππ → ππ, where the first step involves the weak operators Q 6 or Q 8 to O(p 2 /N c) and the second process is the strong pion-pion scattering. The large dependence of the cutoff resides on the contact π − π scattering which is known to have a bad high-energy behaviour violating unitarity …