Description

The SVT trigger has already proved is effectiveness in the selection of fully hadronic $B$ and $D$ meson decays. The trigger selection, requiring the presence of displaced tracks to select the event, affects the proper decay time distribution of the reconstructed mesons. This effect have to be understood and correctly incorporated in the probability density functions used to build up the likelihood needed to extract the lifetime.
This analysis propose a Monte Carlo based method which makes full use of the realistic simulation of the CDF detector and trigger systems. The idea is to extract an efficiency distribution for each decay mode from the simulation and fit those distributions to obtain a functional form expressed as a function of reconstructed proper time.
The method is tested on Data using $B^{+}$ mesons decaying into $B^{+}\rightarrow J/\psi K^+$. These decays have been collected using the $J/\psi$ trigger, where there is no bias from the SVT trigger. We perform the full analysis both using the full dataset, and on the subset of the events obtained after having applied the SVT trigger requirements. Even if the statistic available after the trigger requirements is poor (  400 events) the successful result of test gives us confidence on the method.
After that, we perform the lifetime measurements of $B^+$ and $B^0$ mesons, in the $B^+\to \bar{D}^{0}\pi^{+}$, $B^0\to {D}^{-}\pi^{+}$ and $B^0\to {D}^{-}\pi^+\pi^-\pi^{+}$, decay modes respectively. The positive comparison with the PDG expectations of the lifetime measurements for these two high statistic modes, allowed us to apply the same technique for the $B_s\to D_s^-\pi^+$ and $B_s\to D_s^-\pi^+\pi^-\pi^+$, decay modes, with the $D_s^-$ meson decaying in $\phi\pi^-\to K^+K^-\pi^-$.
All the measurements make use of the improved $L00$ tracking.
The measurements are extracted using a combined mass - lifetime unbinned maximum likelihood fit with per event $\sigma_{ct}$. A Mass-only fit is first performed on a wide mass window to fix the different contributions, then we moved to a narrower mass region to perform the combined fit.
The Large Window mass fit is intended to fix the relative contribution fractions and the combinatorial shape parameters. Then the proper time background contribution is modeled using the high mass side band. Finally in a narrower mass region, the combined mass-lifetime fit is performed.
Different sources of systematic errors are taken into account. The overall contribution is less then 5 $\mu m$.