Measurement of the ratios of branching fractions B(Bs0→Ds- π+π+π-)/B(B0→D-π+π+π-) and B(Bs0→Ds-π+)/ B(B0→D-π+)

Using 355  pb-1 of data collected by the CDF II detector in pp collisions at √s=1.96  TeV at the Fermilab Tevatron, we study the fully reconstructed hadronic decays B(s)0→D(s)-π+ and B(s)0→D(s)-π+π+π-. We present the first measurement of the ratio of branching fractions B(Bs0→Ds-π+π+π-)/B(B0→D-π+π+π-)=1.05±0.10(stat)±0.22(syst). We also update our measurement of B(Bs0→Ds-π+)/B(B0→D-π+) to 1.13±0.08(stat)±0.23(syst), improving the statistical uncertainty by more than a factor of 2. We find B(Bs0→Ds-π+)=[3.8±0.3(stat)±1.3(syst)]×10-3 and B(Bs0→Ds-π+π+π-)=[8.4±0.8(stat)±3.2(syst)]×10-3.