RbandRcin 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 with flavor-changing scalar currents (FCSC's). 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 that are difficult to reconcile with the constraints from $b\to s\gamma \mathrm{and} \rho$. If we treat the couplings of the model as purely phenomenological, then the model can still survive albeit in a rather narrow region of the parameter space. Noting that aspects of the experimental analysis for $R_b$ and $R_c$ may be of some concern, we also disregard $R_b^{\mathrm{expt}}$ and $R_c^{\mathrm{expt}}$ and give predictions for these using constraints from $b\to s\gamma$ and the $\rho$ parameter only. We emphasize the theoretical and experimental advantages of the observable $R_{b+c}\equiv \frac{\Gamma (Z\to b\overline{b} or c\overline{c})}{\Gamma (Z\to \mathrm{hadrons})}$. We also stress the role of $R_l\equiv \frac{\Gamma (Z\to \mathrm{hadrons})}{\Gamma (Z\to l^{+}{l}^{-})}$ in testing the standard model despite its dependence on QCD corrections. Noting that in models with FCNC's the amplitude for $Z\to c\overline{c}$ receives a contribution which grows with $m_t^2$ the importance and uniqueness of precision $Z\to c\overline{c}$ measurements for constraining flavor-changing $t\overline{c}$ currents is underscored.