First Measurement of the Ratio of Branching Fractions BR(LAMBDAB to Lambdac Mu Nu)/BR(LAMBDAB to Lambdac Pi) at CDF II

We present the first measurement of the ratio of branching fractions BR(LAMBDAB TO LAMBDAC MU NU)/BR(LAMBDAB to LAMBDAC PI) based on 171.5 pb-1 of ppbar collisions at the center of mass energy 1.96 TeV taken with the CDF-II detector. In addition, we present measurements of BR(B0 TO DSTAR MU NU)/BR(B0 TO DSTAR PI) and BR(B0 TO D MU NU)/BR(B0 TO D PI), which serve as control samples to understand the data and Monte Carlo used for the Lambdab analysis. We find the relative branching fractions of the control samples are consistent with the ratios obtained by the Particle Data Group at the 0.7 and 1.1 sigma level, respectively. Finally, we obtain the relative Lambdab branching fraction to be: BR(LAMBDAB TO LAMBDAC MU NU)/BR(LAMBDAB to LAMBDAC PI)=20.0 +- 3.0 (stat) +- 1.2 (syst) + 0.7 -2.1 (BR) +- 0.5 (UBR). The uncertainties of the three relative branching fractions are from statistics, CDF internal systematics, external measured branching ratios and unmeasured branching ratios, respectively. We present a method to derive BR(LAMBDAB TO LAMBDAC PI) using previous CDF measurements and obtain BR(LAMBDAB TO LAMBDAC PI) = (0.41 +- 0.19 (stat + syst) + 0.06 -0.08 (pt))%, where the last uncertainty is due to the measured Lambdab pt spectrum. Combining with our result, we determine the exclusive semileptonic branching fraction for the Lambdab= (8.1 +- 1.2 (stat) + 1.1 -1.6 (syst) +- 4.3 (BR(LAMBDAB TO LAMDAC PI)))%