Width difference in the [Formula presented] system

We use the heavy quark expansion to investigate the width difference [Formula presented] between the [Formula presented] mass eigenstates. The corrections of [Formula presented] and [Formula presented] to the leading-order expression in the operator product expansion are derived and estimated to yield a sizable reduction of the leading result for [Formula presented] by typically 30%. For completeness we also quantify small effects due to penguin operators and CKM-suppressed contributions. Based on our results we discuss the prediction for [Formula presented] with particular emphasis on theoretical uncertainties. We find [Formula presented], where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about 10% in [Formula presented] should be within reach, assuming continuing progress in lattice calculations. In addition, we address phenomenological issues and implications of a [Formula presented] measurement for constraints on [Formula presented] and CKM parameters. We further consider in some detail the lifetime ratio [Formula presented] and estimate that, most likely, [Formula presented].