  Measurements of $b$ hadron production ratios in proton-proton collisions at a
centre-of-mass energy of 7 TeV with an integrated luminosity of 3 pb$^{-1}$ are
presented. We study the ratios of strange $B$ meson to light $B$ meson
production $f_s/(f_u+f_d)$ and $\Lambda_b^0$ baryon to light $B$ meson
production $f_{\Lambda_b}/(f_u+f_d)$ as a function of the charmed hadron-muon
pair transverse momentum $p_T$ and the $b$ hadron pseudorapidity $\eta$, for
$p_T$ between 0 and 14 GeV and $\eta$ between 2 and 5. We find that
$f_s/(f_u+f_d)$ is consistent with being independent of $p_{\rm T}$ and $\eta$,
and we determine $f_s/(f_u+f_d)$ = 0.134$\pm$ 0.004 $^{+0.011}_{-0.010}$, where
the first error is statistical and the second systematic. The corresponding
ratio $f_{\Lambda_b}/(f_u+f_d)$ is found to be dependent upon the transverse
momentum of the charmed hadron-muon pair, $f_{\Lambda_b}/(f_u+f_d)=(0.404\pm
0.017 (stat) \pm 0.027 (syst) \pm 0.105 (Br))\times[1 -(0.031 \pm 0.004 (stat)
\pm 0.003 (syst))\times p_T(GeV)]$, where Br reflects an absolute scale
uncertainty due to the poorly known branching fraction Br(\Lambda_c^+ \to
pK^-\pi^+)$. We extract the ratio of strange $B$ meson to light neutral $B$
meson production $f_s/f_d$ by averaging the result reported here with two
previous measurements derived from the relative abundances of $\bar{B}_s \to
D_S^+ \pi ^-$ to $\bar{B}^0 \to D^+K^-$ and $\bar{B}^0 \to D^+\pi^-$. We obtain
$f_s/f_d=0.267^{+0.021}_{-0.020}$.

High Energy Physics - Experiment