$\overrightarrow{B}\phi K_S$ and supersymmetry

The rare decay $\overrightarrow{B}\phi K_S$ is a well-known probe of physics beyond the standard model because it arises only through loop effects yet has the same time-dependent CP asymmetry as $\overrightarrow{B}\psi K_S.$ Motivated by recent data suggesting new physics in $\overrightarrow{B}\phi K_S,$ we look to supersymmetry for possible explanations, including contributions mediated by gluino loops and by Higgs bosons. Chirality-preserving LL and RR gluino contributions are generically small, unless gluinos and squarks masses are close to the current lower bounds. Higgs contributions are also too small to explain a large asymmetry if we impose the current upper limit on ${B(B}_s\to {\mu }^{+}{\mu }^{-}).\mathrm{}$ On the other hand, chirality-flipping LR and RL gluino contributions can provide sizable effects and while remaining consistent with related results in $\overrightarrow{B}\psi K_S,$ $\Delta M_s,$ $\overrightarrow{B}{X}_s\gamma$ and other processes. We discuss how the LR and RL insertions can be distinguished using other observables, and we provide a string-based model and other estimates to show that the needed sizes of mass insertions are reasonable.