Search for $\mathit{T}$ and $\mathit{CP}$ Violation in ${\mathit{B}}^0-{\overline{\mathit{B}}}^0$ Mixing with Inclusive Dilepton Events

We report the results of a search for $T$ and $\mathrm{CP}$ violation in $B^0-{\overline{B}}^0$ mixing using an inclusive dilepton sample collected by the BABAR experiment at the PEP-II $B$ Factory. The asymmetry between ${\ell }^{+}{\ell }^{+}$ and ${\ell }^{-}{\ell }^{-}$ events allows us to compare the probabilities for ${\overline{B}}^0\to B^0$ and $B^0\to {\overline{B}}^0$ oscillations and thus probe $T$ and $\mathrm{CP}$ invariance. Using a sample of $23\times {10}^6$ $B\overline{B}$ pairs, we measure a same-sign dilepton asymmetry of $A_{T/CP}=[0.5\pm 1.2(\mathrm{stat})\pm 1.4(\mathrm{syst}\left)\right]\%$. For the modulus of the ratio of complex mixing parameters $p$ and $q$, we obtain $|q/p|=0.998\mathrm{}\pm 0.006\left(\mathrm{stat}\right)\pm 0.007\left(\mathrm{syst}\right)$.