Amplitude analysis and measurement of the time-dependent CP asymmetry of $B^0 \to K_0^S K_0^S K_0^S$ decays

We present the first results on the Dalitz-plot structure and improved measurements of the time-dependent CP-violation parameters of the process $B^0 \rightarrow K^0_S K^0_S K^0_S$ obtained using $468\times10^{6}$ $B\bar{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. The Dalitz-plot structure is probed by a time-integrated amplitude analysis that does not distinguish between $B^0$ and $\bar{B}^0$ decays. We measure the total inclusive branching fraction ${\cal B}($B^0$ \rightarrow K^0_S K^0_S K^0_S)=\rm (6.19 \pm 0.48 \pm 0.15 \pm 0.12)\times 10^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third represents the Dalitz-plot signal model dependence. We also observe evidence for the intermediate resonant states $f_0(980)$, $f_0(1710)$, and $f_2(2010)$. Their respective product branching fractions are measured to be $\rm(2.70\,^{+1.25}_{-1.19} \pm 0.36 \pm 1.17)\times 10^{-6}$, $\rm(0.50\,^{+0.46}_{-0.24} \pm 0.04 \pm 0.10)\times 10^{-6}$, and $\rm(0.54\,^{+0.21}_{-0.20} \pm 0.03 \pm 0.52)\times 10^{-6}$. Additionally, we determine the mixing-induced CP-violation parameters to be ${\cal S} = -0.94\,^{+0.24}_{-0.21} \pm 0.06 $ and ${\cal C} = -0.17 \pm 0.18 \pm 0.04 $, where the first uncertainty is statistical and the second is systematic. These values are in agreement with the standard model expectation. For the first time, we report evidence of CP violation in $B^0$ \rightarrow K^0_S K^0_S K^0_S$ decays; CP conservation is excluded at 3.8 standard deviations including systematic uncertainties.