Measurement of $b$~Quark Fragmentation Fractions in $p\bar p$ Collisions at $\sqrt{s} = 1.96$~TeV

Using $p\bar p$ collision data at $\sqrt{s} = 1.96$~TeV collected with the CDF\,II experiment at the Fermilab Tevatron collider, we present measurements of the fragmentation fractions $f_u$, $f_d$, $f_s$ and $f_{baryon}$ of produced $b$ quarks that yield $B^+$, $B0$, $B0_s$ and $\Lambda_b$ hadrons. Using a data sample enriched in semileptonic $B$ hadron decays, we reconstruct five lepton-charm final states, $\ell D0$, $\ell D^+$, $\ell D^*+$, $\ell D^+_s$ and $\ell \Lambda_c$ to obtain precise measurements of $f_u / f_d$, $f_s / (f_u+f_d)$ and $f_{baryon} / (f_u+f_d)$.