Has New Physics already been seen in B_d meson decays?

We show using a model independent approach that the deviation in measured B_d^0-\bar{B}_d^0 mixing phase caused by pollution from another amplitude, within the Standard Model, is always less in magnitude, and has the same sign as the weak phase of the polluting amplitude. The exception is to have large destructive interference between the two amplitudes. We demonstrate that any deviation larger than a few degrees is only possible if the observed decay rate results from fine tuned cancellations between significantly larger quark level amplitudes. These simple observations have very significant consequences for signals of New Physics.