A density-matrix method for the study of tagged states of neutral B mesons with arbitrary coherence properties is applied to several examples, including e + e − production both at and above the Υ(4S) resonance, and hadronic production. In the absence of coherence the only term modulating the exponential decay of a neutral B meson behaves as cos ∆mt, while a sin ∆mt modulation is a signal of partial or full coherence. Decays to CP eigenstates are needed to fully specify the density matrix. We relate these results to more familiar expressions for the cases of the Υ(4S) and incoherent production.
I IntroductionNeutral B mesons undergo time-dependent oscillations with their antiparticles. This feature, first demonstrated for neutral kaons nearly half a century ago [1], has been crucial in extracting fundamental information on the mechanism of CP violation from the decays of neutral B's. Moreover, the oscillations themselves have provided crucial information on the magnitude of electroweak couplings, and were one of the first pieces of evidence for a very heavy top quark [2].The oscillations are characterized by splittings ∆m between mass eigenstates. For the B d =bd, the most recent world average [3] is ∆m d = 0.487 ± 0.014 ps −1 . For the B s =bs, only a lower limit [3,4] ∆m s > 15 ps −1 exists at present.1 To be submitted to Phys. Rev. D.