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The lifetime of the $B^{0}_{s}$ meson is measured in the decay channel$B^{0}_{s} \to J/\psi\mbox{ }\pi^+ \pi^-$ with $880 \leq M_{\pi^+\pi^-} \leq1080$ MeV/$c^2$, which is mainly a CP-odd state and dominated by the$f_{0}(980)$ resonance. In 10.4 fb$^{-1}$ of data collected with the D0detector in Run II of the Tevatron, the lifetime of the $B^{0}_{s}$ meson ismeasured to be $\tau(B^{0}_{s}) = 1.70\pm 0.14 \mbox{ (stat)} \pm 0.05 \mbox{(syst) ps}$. Neglecting CP violation in $B_s^0/\bar{B}_s^0$ mixing, themeasurement can be translated into the width of the heavy mass eigenstate ofthe $B^0_s$, $\Gamma_H = 0.59 \pm 0.05 \mbox{ (stat)} \pm 0.02 \mbox{ (syst)}\mbox{ ps$^{-1}$}$.

$B^{0}_{s}$ lifetime measurement in the CP-odd decay channel $B^{0}_{s} \to J/\psi\mbox{ }f_{0}(980)$