A search for the exotic meson $X(5568)$ decaying into the $B^0_s pi^{pm}$
final state is performed using data corresponding to $9.6 extrm{fb}^{-1}$
from $p{ar p}$ collisions at $sqrt{s} = 1960$ GeV recorded by the Collider
Detector at Fermilab. No evidence for this state is found and an upper limit of
6.7\% at the 95\% confidence level is set on the fraction of $B^0_s$ produced
through the $X(5568)
ightarrow B^0_s , pi^{pm}$ process.
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