B-B-bar mixing involves three physical parameters: the magnitudes of the
off-diagonal elements of the mass and decay matrices and their relative
phase. They are related to the mass and width differences between the
mass eigenstates and to the CP asymmetry in flavour-specific decays,
a_fs. Introducing a new operator basis I present new, more precise
theory predictions for the width differences in the B_s and B_d systems:
in the Standard Model one finds Delta Gamma_s = 0.088 +/- 0.017 ps^{-1}
and Delta Gamma_d = (26.7 +5.8/-6.5) * 10^{-4} ps^{-1}. Updates
of the mass differences Delta M_d and Delta M_s and of a_{fs}^d and
a_{fs}^s are also presented. Then I discuss how various present and
future measurements can be combined to constrain new physics. The
extraction of a new CP phase phi_s^Delta from data on a_{fs}^s also
profits from our new operator basis. Confronting our new formulae with
D0 data we find that sin phi_s^Delta deviates from zero by 2 sigma.