$R_b$ and $R_c$ in the Two Higgs Doublet Model with Flavor Changing Neutral Currents

A study of $R_b$ and $R_c$ is presented in the context of a Two Higgs Doublet Model (2HDM) with flavor changing scalar currents (FCSC). Implications of the model for the $\rho$-parameter and for $b\to s\gamma$ are also considered. The experimental data on $R_b$ places stringent constraints on the model parameters. The configuration of the model needed to account for $R_b$ is found to be irreconcilable with constraints from $b\to s\gamma$ and $\rho$. In particular, if $R^{\rm exp}_b>R^{\sss{\rm SM}}_b$ persists then this version of 2HDM will be ruled out or require significant modifications. Noting that aspects of the experimental analysis for $R_b$ and $R_c$ may be of some concern, we also disregard $R^{\rm exp}_b$ and $R^{\rm exp}_c$ and give predictions for these using constraints from $b\to s\gamma$ and $\rho$ parameter only. We emphasize the theoretical and experimental advantages of the observable $R_{b+c}\equiv \Gamma(Z\to b\bar b\mbox{ or } c\bar c)/\Gamma(Z\to\mbox{hadrons})$. We also stress the role of $R_\ell\equiv \Gamma(Z\to\mbox{hadrons})/\Gamma(Z\to \ell^+\ell^-)$ in testing the Standard Model (SM) despite its dependence on QCD corrections. Noting that in models with FCNC the amplitude for $Z\to c\bar c$ receives a contribution which grows with $m^2_t$, the importance and uniqueness of precision $Z\to c\bar c$ measurements for constraining flavor changing $t\bar c$ currents is underscored.