Constraining New Physics with the Fermilab Measurement ofCPViolation inB→ψKs

Recently, the CDF Collaboration has reported a measurement of the CP asymmetry in the $B\to \psi K_s$ decay: $a_{\psi K_s}{=0.79\mathrm{}}_{-0.44\mathrm{}}^{+0.41\mathrm{}}$. We analyze the constraints that follow from this measurement on the size and the phase of contributions from new physics to $B-\overline{B}$ mixing. Defining the relative phase between the full $M_{12}$ amplitude and the standard model contribution to be $2{\theta }_d$, we find a new bound: $\sin 2{\theta }_d\gtrsim -0.6\mathrm{}(-0.87\mathrm{})$ at $1\sigma$ (95% C.L.). Further implications for the CP asymmetry in semileptonic $B$ decays are discussed.