Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+

We perform amplitude analyses of the decays $B^0\to K^{+}{K}^{-}{K}_S^0$, $B^+ \rightarrow K^+K^-K^+$,and$B^+ \to K^0_S K^0_S K^+$, and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\times {10}^6$ $B\bar{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For $B^{+}\to K^{+}{K}^{-}{K}^{+}$, we find a direct CP asymmetry in $B^{+}\to \varphi (1020)K^{+}$ of $A_{CP}=(12.8\pm 4.4\pm 1.3)$, which differs from zero by $2.8\sigma$. For $B^0\to K^{+}{K}^{-}{K}_S^0$, we measure the CP-violating phase ${\beta }_{\mathrm{e}\mathrm{f}\mathrm{f}}(\varphi (1020)K_S^0)=(21\pm 6\pm 2{)}^{\circ }$. For $B^{+}\to K_S^0{K}_S^0{K}^{+}$, we measure an overall direct CP asymmetry of $A_{CP}=(4_{-5}^{+4}\pm 2)$. 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 $f_0(1500)$, $f_2^{\mathrm{\prime }}(1525)$, and $f_0(1710)$.