Possible Solution to $R_b$ -- $R_c$ Problem

Abstract

We investigate the $R_b$--$R_c$ problem, starting from the more diffcult $R_c$. Introducing an isosinglet charge 2/3 quark $Q$ moves both $R_c$ and $R_b$ in the right direction. If one allows for large $c$-$Q$ {\it and} $t$-$Q$ mixings, then $R_c$ could be reduced because of singlet content of charm quark, while $R_b$ gets enhanced by a light effective top quark mass in the loop. The heavy quark observed at CDF would be dominantly a singlet quark, while the top quark is lighter than $M_W$. It is necessary to introduce a second Higgs doublet, where $H^+$ is heavy while at least one exotic neutral Higgs boson is very light. $H^+$--$h^0$ splitting accounts for $\delta\rho$, while light $h^0$ induce fast $t\to c + h^0$ decay and hides the actual top quark at the Tevatron. The scenario can be immediately tested at LEP II via search for light top production (and toponium!). At Tevatron, one should search for exotic decay modes such as $Q\to Z + X$ or $Q\to H + X$, or measure the BR for the standard $bW$ mode. Light top search should also be renewed.