Using data from proton-antiproton collisions at root s = 1.96 TeV recorded by the CDF II detector at the Fermilab Tevatron, evidence for the excited resonance state Lambda(b)*(0) pi(-) pi(+) is presented in its Lambda(0)(b) pi(-) pi(+) decay followed by the Lambda(0)(b) -> Lambda(+)(c) pi(-) and Lambda(+)(c) -> pK(-) pi(-) decays. The analysis is based on a data sample corresponding to an integrated luminosity of 9.6 fb(-1) collected by an online event selection based on charged-particle tracks displaced from the proton-antiproton interaction point. The significance of the observed signal is 3.5 sigma. The mass of the observed state is found to be 5919.22 +/- 0.76 MeV/c(2) in agreement with similar findings in proton-proton collision experiments.
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