Measurement of the $\Lambda_b$ lifetime in $p\bar{p}$ Collisions at $\sqrt{s}=1.96$ TeV

The lifetime of the $\Lambda_b$ baryon is presently the most interesting of all $b$-hadron lifetimes, and at the same time the least well known experimentally. We study the lifetime of the $\Lambda_b$ baryon using $\Lambda_b \to \Lamdbda_c^+\pi^+$ decay mode in 360~pb$^{-1}$ of CDF data. Our $\Lambda_b \to \Lamdbda_c^+\pi^+$ sample has in excess of $1400$ events and is the largest sample of $\Lambda_b$ decays in existence. We study the effects of the trigger bias and the presence of physics backgrounds on the measurement of the lifetime of $\Lambda_b$.