How Devious are Deviations From Quantum Mechanics: The Case of the B^0 \bar B^0 System

Considering semileptonic decays of the entangled B^0 \bar B^0 state which is generated in the decay of Upsilon(4S), we simply multiply the quantum-mechanical interference term by a factor (1-\zeta) and use the ``decoherence parameter'' \zeta as a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic B^0 \bar B^0 decays. In particular, we show that when confronted with the experimental values of the ratio R=(# like-sign dilepton events)/(# opposite-sign dilepton events) and of the B_H--B_L mass difference, the ensuing one standard deviation range of the decoherence parameter depends strongly on the basis in the B^0--\bar B^0 space used to build the entangled B^0 \bar B^0 state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.