Measurement of $B$ Meson Lifetimes Using a Monte Carlo Independent Approach

We present a measurement of the $B^+$ and $B^0$ lifetime in the fully reconstructed decay modes $B^+ \to D^0 \pi^+$ and $B^0 \to D^+ \pi^-$ with $D^0 \to K \pi$ and $D^+ \to K \pi \pi$, respectively. We use 1~fb$^{-1}$ of data taken with the CDF\,II detector using the high impact parameter trigger. A lifetime bias is introduced by the trigger. This bias is accounted for by a calculation of the exact acceptance function on an event by event basis without the need to use Monte-Carlo simulation to model this bias.