Effect of Penguin Operators in theB0→J/ψK0CPAsymmetry

Performing a fit to the available experimental data, we quantify the effect of long-distance contributions from penguin contractions in $B^0\to J/\psi K^0$ decays. We estimate the deviation of the measured ${\mathcal{S}}_{CP}$ term of the time-dependent $CP$ asymmetry from $\sin 2\beta$ induced by these contributions and by the penguin operators. We find $\Delta \mathcal{S}\equiv {\mathcal{S}}_{CP}(J/\psi K)-\sin 2\beta =0.000\pm 0.012$ ($[-0.025,0.024]@95\%$ probability), an uncertainty much larger than previous estimates and comparable to the present systematic error quoted by the experiments at the $B$ factories.