Implications of the evidence for direct <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> violation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> 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.