Final result:

$$\frac{ BR(D^+ \rightarrow K\pi\pi) }{ BR(\Lambda_c^+ \rightarrow pK\pi) } = 1.84 \pm 0.493$$ (5)

$${ N_{\Lambda_b} }= 214 \pm 19(stat.)$$ (6)

$${ N_{\bar{B}^0} } = 790 \pm 32(stat.)$$ (7)

$$\frac{ N_{\Lambda_b} }{ N_{\bar{B}^0} } = 0.27 \pm 0.03(stat.)$$ (8)

$$\frac{ \epsilon_{\bar{B}^0} }{ \epsilon_{\Lambda_b} } = 1.65$$ (9)

The CDF systematic errors (including the statistical error on the ratio of reconstruction efficiencies) combine to give: $+13.6\%$, $-13.3\%$.

Putting together Eqs. (5), (8) and (9), one obtains

$$\frac{ \sigma_{\Lambda^{0}_{b}}(p_T > 6)}{ \sigma_{\overline... ...0.08\mbox{ (stat)} \pm 0.11\mbox{ (syst)} \pm 0.22\mbox{ (BR)}$$ (10)

where the final source of error is due to the uncertainty on the $\Lambda^{+}_{c}\rightarrow pK\pi$ branching ratio.

For comparison, making the assumption that:

$$\frac{f_{\Lambda_b}}{f_d} \sim \frac{ \sigma_{\Lambda^{0}_{b}}(p_T > 6)}{ \sigma_{\overline{B^{0}}}(p_T > 6)}$$ (11)

and using the 2004 PDG fragmentation ratio $f_{baryon}/f_{d} = 0.249 \pm 0.043$ is used to extract relative braching ratio

$$\frac{ BR(\Lambda_b \rightarrow \Lambda_c^+\pi^-) } { BR(\ba... ....3\mbox{ (stat)} \pm 0.4 \mbox{ (syst)} \pm 1.1\mbox{ (BR+FR)}$$ (12)