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 ¯ B 0 state which is generated in the decay of Υ(4 S ), we simply multiply the quantum-mechanical interference term by a factor (1 − ζ ) and use the “decoherence parameter” ζ as a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic B 0 ¯ 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 – ¯ B 0 space used to build the entangled B 0 ¯ B 0 state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.