Study ofCPviolation in Dalitz-plot analyses ofB0→K+K−KS0,B+→K+K−K+, andB+→KS0KS0K+

We perform amplitude analyses of the decays ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}_{S}^{0}$, ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{+}$, and ${B}^{+}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{S}^{0}{K}^{+}$, and measure $CP$-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{+}$, we find a direct $CP$ asymmetry in ${B}^{+}\ensuremath{\rightarrow}\ensuremath{\phi}(1020){K}^{+}$ of ${A}_{CP}=(12.8\ifmmode\pm\else\textpm\fi{}4.4\ifmmode\pm\else\textpm\fi{}1.3)%$, which differs from zero by $2.8\ensuremath{\sigma}$. For ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}_{S}^{0}$, we measure the $CP$-violating phase ${\ensuremath{\beta}}_{\mathrm{eff}}(\ensuremath{\phi}(1020){K}_{S}^{0})=(21\ifmmode\pm\else\textpm\fi{}6\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{}$. For ${B}^{+}\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{S}^{0}{K}^{+}$, we measure an overall direct $CP$ asymmetry of ${A}_{CP}=({4}_{\ensuremath{-}5}^{+4}\ifmmode\pm\else\textpm\fi{}2)%$. We also perform an angular-moment analysis of the three channels and determine that the ${f}_{X}(1500)$ state can be described well by the sum of the resonances ${f}_{0}(1500)$, ${f}_{2}^{\ensuremath{'}}(1525)$, and ${f}_{0}(1710)$.