Measurement of the ${\overline{B}}_s^0$ Effective Lifetime in the $J/\psi f_0(980)$ Final State

The effective lifetime of the ${\overline{B}}_s^0$ meson in the decay mode ${\overline{B}}_s^0\to J/\psi f_0(980)$ is measured using $1.0{\mathrm{fb}}^{-1}$ of data collected in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ with the LHCb detector. The result is $1.700\pm 0.040\pm 0.026\mathrm{ps}$, where the first uncertainty is statistical and the second systematic. As the final state is $CP$-odd, and $CP$ violation in this mode is measured to be small, the lifetime measurement can be translated into a measurement of the decay width of the heavy ${\overline{B}}_s^0$ mass eigenstate, ${\Gamma }_H=0.588\pm 0.014\pm 0.009{\mathrm{ps}}^{-1}$.

Figure 1

Invariant mass distributions of selected (a) ${\pi }^{+}{\pi }^{-}$ and (b) $K^{-}{\pi }^{+}$ combinations (solid histograms) for events within $\pm 20\mathrm{MeV}$ of the respective ${\overline{B}}_s^0$ and ${\overline{B}}^0$ mass peaks. Backgrounds (dashed histograms) are determined by fitting the $J/\psi {\pi }^{+}{\pi }^{-}$ ($J/\psi K^{-}{\pi }^{+}$) mass in bins of ${\pi }^{+}{\pi }^{-}$ ($K^{-}{\pi }^{+}$) mass. Regions between the arrows are used in the subsequent analysis.

Figure 2

Ratio of decay time acceptances between ${\overline{B}}_s^0\to J/\psi f_0(980)$ and ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}$ decays obtained from simulation. The solid (blue) line shows the result of a linear fit.

Figure 3

Invariant mass distributions of selected (a) $J/\psi {\pi }^{+}{\pi }^{-}$ and (b) $J/\psi K^{-}{\pi }^{+}$ candidates. The solid (blue) curves show the total fits, the long dashed (purple) curves show the respective ${\overline{B}}_s^0\to J/\psi f_0(980)$ and ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}$ signals, and the dotted (gray) curve shows the combinatorial background. In (a) the short dashed (light blue-green) curve shows the ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ background and the dash dotted (green) curve shows the ${\overline{B}}^0\to J/\psi K^{-}{\pi }^{+}$ reflection. In (b) the short dashed (red) curve near 5370 MeV shows the ${\overline{B}}_s^0\to J/\psi K^{-}{\pi }^{+}$ background.

Figure 4

Decay time distributions for (a) ${\overline{B}}_s^0\to J/\psi f_0(980)$ and (b) ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}$. In (b) the error bars are smaller than the points.

Figure 5

Decay time ratio between ${\overline{B}}_s^0\to J/\psi f_0(980)$ and ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}$, and the fit for ${\Delta }_{J/\psi f_0}$.