High Scale Study of Possible B \to \phi K_S CP Physics

Some rare decay processes are particularly sensitive to physics beyond the Standard Model (SM) because they have no SM tree contributions. We focus on one of these, $B_{d}\to \phi K_{s}$. Our study is in terms of the high scale effective theory, and high scale models for the underlying theory, while previous studies have been focusing on the low scale effective Lagrangian. We examine phenomenologically the high scale parameter space with full calculations, but largely report the results in terms of mass insertion techniques since they are then easily pictured. We also determine the ranges of different mass insertions that could produce large non-SM CP effects. Then we exhibit classes of high scale models that can or cannot provide large non-SM CP effects, thus demonstrating that data on $B_{d}\to \phi K_{s}$ can probe both supersymmetry breaking and the underlying high scale theory and even make relatively direct contact with string-motivated models. We provide a novel and systematic technique to understand the relations between high and low scale parameters from RGE running. We include all constraints from other data, particularly $b\to s\gamma$ and EDMs.