Measurement of $B_d^0-{\overline{B}}_d^0$ Mixing Rate from the Time Evolution of Dilepton Events at the $\mathit{\Upsilon }\left(4\mathit{S}\right)$

We report a determination of the $B_d^0-{\overline{B}}_d^0$ mixing parameter $\Delta m_d$ based on the time evolution of dilepton yields in $\Upsilon \left(4S\right)$ decays. The measurement is based on a $5.9{\mathrm{fb}}^{-1\mathrm{}}$ data sample collected by the Belle detector at KEKB. The proper-time difference distributions for same-sign and opposite-sign dilepton events are simultaneously fitted to an expression containing $\Delta m_d$ as a free parameter. Using both muons and electrons, we obtain $\Delta m_d=0.463\mathrm{}\pm 0.008\left(\mathrm{stat}\right)\pm 0.016\left(\mathrm{syst}\right){\mathrm{ps}}^{-1\mathrm{}}$. This is the first determination of $\Delta m_d$ from time evolution measurements at the $\Upsilon \left(4S\right)$. We also place limits on possible $\mathrm{CPT}$ violations.