  Exchange of unparticle stuff of dimension $d_\U$ with FCNC interaction can
induce $M^{12,u}$ and $\Gamma^{12,u}$ causing meson and anti-meson mixing with
the relation $\Gamma^{12,u}/M^{12,u} = 2 \tan(\pi d_\U)$. We show that this
type of unparticle contribution can provide the much needed large
$\Gamma^{12}_s$ to explain the recently observed anomalously large dimuon
asymmetry in $B_s -\bar B_s$ system reported by D0 collaboration. The same
interaction can also accommodate large mixing induced CP violation in $B_s \to
J/\psi \phi$ indicated by CDF and D0 data. Experimental data can provide
constraints on the unparticle dimension and scale.
