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The analysis uses data from an integrated luminosity of approximately 172pb-1 of ppbar collisions at sqrt(s)=1.96 TeV, collected with the CDF IIdetector at the Fermilab Tevatron. The Lambda_b and B0 relative branchingfractions are measured to be: B(Lambda_b to Lambda_c+ mu nu)/B(Lambda_b toLambda_c+ pi) = 16.6 +- 3.0 (stat) +- 1.0 (syst) +2.6 -3.4 (PDG) +- 0.3 (EBR),B(B0 to D+ mu nu)/B(B0 to D+ pi) = 9.9 +- 1.0 (stat) +- 0.6 (syst) +- 0.4 (PDG)+- 0.5 (EBR), B(B0 to D*+ mu nu)/B(B0 to D*+ pi) = 16.5 +- 2.3 (stat) +- 0.6(syst) +- 0.5 (PDG) +- 0.8 (EBR) This article also presents measurements of thebranching fractions of four new Lambda_b semileptonic decays: Lambda_b toLambda_c(2595)+ mu nu, Lambda_b to Lambda_c(2625)+ mu nu, Lambda_b toSigma_c(2455)0 pi mu nu, Lambda_b to Sigma_c(2455)++ pi mu nu, relative to thebranching fraction of the Lambda_b to Lambda_c mu nu decay. Finally, thetransverse-momentum distribution of Lambda_b baryons produced in p-pbarcollisions is measured and found to be significantly different from that of B0mesons.

First Measurement of the Ratio of Branching Fractions B(Lambda_b to Lambda_c mu nu)/B(Lambda_b to Lambda_c pi)