We study the charmless decays B to Lambda Lambdabar h, where h stands for pi^+, K^+,K^0,K^{*+}, or K^{*0}, using a 605 fb^{-1} data sample collected at the Upsilon(4S)resonance with the Belle detector at the KEKB asymmetric energy e^+ e^- collider. We observe B0 to Lambda Lambdabar K0 and B0 to Lambda Lambdabar K*0 with branching fractions of (4.76^{+0.84}_{-0.68} (stat.) pm 0.61 (syst.)) times 10^{-6} and (2.46^{+0.87}_{-0.72} pm 0.34) times 10^{-6}, respectively. The significances of these signals in the threshold-mass enhanced mass region are 12.4 sigma and 9.3 sigma, respectively. We also update the branching fraction BF(B+ to Lambda Lambdabar K+) = (3.38^{+0.41}_{-0.36} pm 0.41)times 10^{-6} with better accuracy,and report the following measurement or 90% confidence level upper limit in the threshold-mass-enhanced region: BF(B+ to Lambda Lambdabar K*+) = (2.19^{+1.13}_{-0.89} pm 0.33) times 10^{-6} with 3.7 sigma significance; BF(B+ to Lambda Lambdabar pi+) < 0.94 times 10^{-6}. A related search for B0 to Lambda Lambdabar D0bar yields a branching fraction BF(B0 to Lambda Lambdabar D0bar) = (1.05_{-0.44}^{+0.57} pm 0.13)times 10^{-5}. This may be compared with the large, ~10^{-4}, branching fraction observed for B0 to p pbar D0bar. The m_{Lambda Lambdabar} enhancements near threshold and related angular distributions for the observed modes are also reported. PACS:13.25.Hw, 14.40.Nd
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