Simultaneous measurement of the ratio $ {\cal {B}}( t\rightarrow Wb )/{\cal{B}}(t\rightarrow Wq )$ and the top quark pair production cross section with the D0 detector at $ \sqrt{s}=1.96$~TeV

We present the first simultaneous measurement of the ratio of branching fractions, $R={\cal{B}}(t \rightarrow Wb)/{\cal{B}}(t \rightarrow Wq)$, with $q$ being a $d$, $s$, or $b$ quark, and the top quark pair production cross section $\sigma_{t\bar{t}}$ in the lepton plus jets channel using $0.9~\mathrm{fb}^{-1}$ of $p\bar{p}$ collision data at $\sqrt{s}=1.96$~TeV collected with the D0 detector. We extract $R$ and $\sigma_{t\bar{t}}$ by analyzing samples of events with 0, 1 and $\ge 2$ identified $b$ jets.