Implications of the evidence for direct C P violation in D → π + π − decays

The observation of C P violation in the difference of C P asymmetries between D → K + K − and D → π + π − has raised a debate whether the observed asymmetries can be regarded as a signal of physics beyond the standard model (SM). In this paper we obtain all the topological amplitudes and isospin amplitudes directly from measured observables for D → π π . These results unambiguously imply a very large penguin contribution, having a central value 4.74 times the magnitude of the amplitude for D 0 → π + π − . This fitted central value differs from a reasonable SM estimate of 10% with a significance greater than 3.3 σ . In contrast to previous studies, we present model-independent arguments based only on unitarity of rescattering amplitudes to show that large penguins cannot arise from rescattering alone and likely indicate physics beyond the SM. In a model-independent approach we show how a very small contribution from physics beyond the SM with a large weak phase alleviates the problem.