A model for decoherence of entangled beauty

Abstract

In the context of the entangled $B^0{\bar{B}}^0$ state produced at the ${\rm Y}(4S)$ resonance, we consider a modification of the usual quantum-mechanical time evolution with a dissipative term, which contains only one parameter denoted by $\lambda$ and respects complete positivity. In this way a decoherence effect is introduced in the time evolution of the 2-particle $B^0{\bar{B}}^0$ state, which becomes stronger with increasing distance between the two particles. While our model of time evolution has decoherence for the 2-particle system, we assume that, after the decay of one of the two B mesons, the resulting 1-particle state obeys the purely quantum-mechanical time evolution. From the data on dilepton events we derive an upper bound on $\lambda$. We also show how $\lambda$ is related to the so-called ``decoherence parameter'' $\zeta$, which parameterizes decoherence in neutral flavoured meson--antimeson systems.

Comments: 11 pages, revtex. Two references and some comments added, version to be published in Phys. Rev. D