  Using the hadronic matrix elements from the lattice, B_K and xi_s, involving
only the 4-quark operators for Delta flavor (F) = 2 Hamiltonian relevant for K,
B_d and B_s mixing, along with V_cb, we deduce a non-trivial constraint on the
SM, sin (2 beta) = 0.87+-0.09. This deviates from direct experimental
measurements via the tree process, b -> c c s as well as the one via the
penguin-loop b -> s decays by around 2.1 and 2.7 sigma respectively. If these
deviations are confirmed they would imply the presence of new physics rather
pervasively in both B_d mixing (i.e. very likely in b -> d) as well as in b ->
s transitions requiring a beyond the SM CP-odd phase. Consequently,
improvements in the relevant lattice calculations should be given a high
priority.
