Limits on the Decay-Rate Difference of Neutral $B$ Mesons and on $CP$, $T$, and $CPT$ Violation in $B^0{\overline{B}}^0$ Oscillations

Using events in which one of two neutral $B$ mesons from the decay of an ${\rm Y}(4S)$ meson is fully reconstructed, we determine parameters governing decay $(\Delta {\Gamma }_d/{\Gamma }_d)$, $CP$, and $T$ violation ($|q/p|$), and $CP$ and $CPT$ violation ($\mathrm{Re}\mathsf{z},\mathrm{Im}\mathsf{z}$). The results, obtained from an analysis of $88\times {10}^6$ ${\rm Y}(4S)$ decays recorded by BABAR, are $\mathrm{sgn}(\mathrm{Re}{\lambda }_{CP})\Delta {\Gamma }_d/{\Gamma }_d=-0.008\pm 0.037(\mathrm{stat})\pm 0.018(\mathrm{syst})[-0.084,0.068],|q/p|=1.029\pm 0.013(\mathrm{stat})\pm 0.011(\mathrm{syst})[1.001,1.057],(\mathrm{Re}{\lambda }_{CP}/|{\lambda }_{CP}|)\mathrm{Re}\mathsf{z}=0.014\pm 0.035(\mathrm{stat})\pm 0.034(\mathrm{syst})[-0.072,0.101],\mathrm{Im}\mathsf{z}=0.038\pm 0.029(\mathrm{stat})\pm 0.025(\mathrm{syst})[-0.028,0.104].$ The values inside the square brackets indicate the 90% confidence-level intervals. These results are consistent with standard model expectations.