Model for decoherence of entangled beauty

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