Measurement of theCP-violation parameter ofB0mixing and decay withpp¯→μμXdata

We measure the dimuon charge asymmetry $A$ in $p\overline{p}$ collisions at a center of mass energy $\sqrt{s}=1960\mathrm{GeV}$. The data was recorded with the D0 detector and corresponds to an integrated luminosity of approximately $1.0{\mathrm{fb}}^{-1}$. Assuming that the asymmetry $A$ is due to asymmetric $B^0\leftrightarrow {\overline{B}}^0$ mixing and decay, we extract the $CP$-violation parameter of $B^0$ mixing and decay: $\frac{\Re ({ϵ}_{B^0})}{1+|{ϵ}_{B^0}{|}^2}=\frac{A_{B^0}}{4}=-0.0023\pm 0.0011(\mathrm{stat})\pm 0.0008(\mathrm{syst}).$ $A_{B^0}$ is the dimuon charge asymmetry from decays of $B^0{\overline{B}}^0$ pairs. The general case, with $CP$ violation in both $B^0$ and $B_s^0$ systems, is also considered. Finally we obtain the forward-backward asymmetry that quantifies the tendency of ${\mu }^{+}$ to go in the proton direction and ${\mu }^{-}$ to go in the antiproton direction. The results are consistent with the standard model and constrain new physics.