Introduction

The CDF II detector can reconstruct significant samples of charmless two-body $B$ decays of interest for the purpose of investigating CP violation [1], by means of a dedicated trigger on impact parameter. While $B_d$ decays are being studied also at leptonic $B$-factories, the $B_s$ modes are currently unique to the Tevatron. Experimentally, the mass peaks of all two-body decays of type $B_{d,s}\rightarrow h^{+}h^{'-}$ (where $h,h'= K,\pi$), when reconstructed with a conventional assignment of pion mass to both prongs, are expected to contribute a number of overlapping peaks, seen collectively as a single unresolved bump in the CDF II data. The current analysis measures the relative branching fractions of the individual decays contributing to the $B_{d,s}\rightarrow h^{+}h^{'-}$ signal, and the direct CP asymmetry in $B^0_d\rightarrow K^+\pi^-$, by exploiting the small kinematics differences between distinct modes and the particle identification information provided by the specific ionization ($dE/dx$) in the drift chamber. The $dE/dx$ measurement was calibrated with a sample of kaons and pions ($h, h^{'}$) from $D^{*}\rightarrow \pi D^0\rightarrow \pi [h^{+}h^{'-}]$ decays. The resulting $K/\pi$ separation is 1.39$\sigma$ (1.43$\sigma$) for negative (positive) tracks (see Fig. ).