  We present a search for the technicolor particles $\rho_{T}$ and $\pi_{T}$ in
the process $p\bar{p} \to \rho_{T} \to W\pi_{T}$ at a center of mass energy of
$\sqrt{s}=1.96 \mathrm{TeV}$. The search uses a data sample corresponding to
approximately $1.9 \mathrm{fb}^{-1}$ of integrated luminosity accumulated by
the CDF II detector at the Fermilab Tevatron. The event signature we consider
is $W\to \ell\nu$ and $\pi_{T} \to b\bar{b}, b\bar{c}$ or $b\bar{u}$ depending
on the $\pi_{T}$ charge. We select events with a single high-$p_T$ electron or
muon, large missing transverse energy, and two jets. Jets corresponding to
bottom quarks are identified with multiple $b$-tagging algorithms. The observed
number of events and the invariant mass distributions are consistent with the
standard model background expectations, and we exclude a region at 95%
confidence level in the $\rho_T$-$\pi_T$ mass plane. As a result, a large
fraction of the region $m(\rho_T) = 180$ - $250 \mathrm{GeV}/c^2$ and $m(\pi_T)
= 95$ - $145 \mathrm{GeV}/c^2$ is excluded.
