Preliminary results for the longitudinal polarization of $Lambda$ and ${bar Lambda}$ hyperons in longitudinally polarized proton-proton collisions at $sqrt s$ = 200 GeV are presented. The $Lambda$($bar Lambda$) candidates are reconstructed at mid-rapidity ($|eta|<1$) with the time projection chamber of the STAR experiment at RHIC, using 0.5 pb$^{-1}$ collected in 2003 and 2004 with beam polarizations of up to 45%. Their mean longitudinal momentum fraction $x_F$ is about 8 $times$$10^{-3}$ and their mean transverse momentum $p_T$ is about 1.5 GeV. The analysis uses asymmetries of counts for different spin states of the colliding proton beams and does not require detailed knowledge of the detector acceptance. The preliminary $Lambda$(${bar Lambda}$) polarization values are consistent with zero within their statistical uncertainties of 0.05.
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