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 p (p) over bar at collisions at root s = 1.96 TeV at the Fermilab Tevatron, we study the fully reconstructed hadronic decays B-(s)(0) -> D-(s)(-)pi(+) and B-(s)(0) -> D-(s)(-) pi(+)pi(+)pi(-). We present the first measurement of the ratio of branching fractions B(B-s(0) -> D-s(-) pi(+)pi(+)pi(-))/B(B-0 -> D-s(-) pi(+)pi(+)pi(-)) = 1.05 +/- 0.10(stat) +/- 0.22(syst). We also update our measurement of B(B-s(0) -> D-s(-)pi(+))/B(B-0 -> D-pi(+)) to 1.13 +/- 0.08(stat) +/- 0.23(syst), improving the statistical uncertainty by more than a factor of 2. We find B(B-s(0) -> D-s(-)pi(+)) = [3.8 +/- 0.3(stat) +/- 1.3(syst)] x 10(-3) and B(B-s(0) -> D-s(-) pi(+)pi(+)pi(-)) = [8.4 +/- 0.8 (stat) +/- 3.2(syst)] x 10(-3).