We report a measurement of the Lambda(0)(b) lifetime in the exclusive decay Lambda(0)(b)-> J/psi Lambda(0) in p (p) over bar collisions at root s=1.96 TeV using an integrated luminosity of 1.0 fb(-1) of data collected by the CDF II detector at the Fermilab Tevatron. Using fully reconstructed decays, we measure tau(Lambda(0)(b))=1.593(-0.078)(+0.083)(stat)+/- 0.033(syst) ps. This is the single most precise measurement of tau(Lambda(0)(b)) and is 3.2 sigma higher than the current world average. RI Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; De Cecco, Sandro/B-1016-2012; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; Azzi, Patrizia/H-5404-2012
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