Search for a Two-Higgs-Boson Doublet Using a Simplified Model inpp¯Collisions ats=1.96 TeV

We present a search for new particles in an extension to the standard model that includes a heavy Higgs boson (${H}^{0}$), a lighter charged Higgs boson (${H}^{\ifmmode\pm\else\textpm\fi{}}$), and an even lighter Higgs boson ${h}^{0}$, with decays leading to a $W$-boson pair and a bottom-antibottom quark pair in the final state. We use events with exactly one lepton, missing transverse momentum, and at least four jets in data corresponding to an integrated luminosity of $8.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected by the CDF II detector in proton-antiproton collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. We find the data to be consistent with standard model predictions and report the results in terms of a simplified Higgs-cascade-decay model, setting 95% confidence level upper limits on the product of cross section and branching fraction from 1.3 pb to 15 fb as a function of ${H}^{0}$ and ${H}^{\ifmmode\pm\else\textpm\fi{}}$ masses for ${m}_{h}^{0}=126\text{ }\text{ }\mathrm{GeV}/{c}^{2}$.