How devious are deviations from quantum mechanics: The case of theB0B0system

Abstract

Considering semileptonic decays of the entangled ${B}^{0}{B}^{0}$ state which is generated in the decay of $\ensuremath{\Upsilon}(4S),$ we simply multiply the quantum-mechanical interference term by a factor $(1\ensuremath{-}\ensuremath{\zeta})$ and use the ``decoherence parameter'' \ensuremath{\zeta} 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=(no. like-sign dilepton events)/(no. opposite-sign dilepton events) and of the ${B}_{H}\ensuremath{-}{B}_{L}$ 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.