Implications of the evidence for direct $\mathbf{CP}$ violation in $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays

Abstract

The observation of $CP$ violation in the difference of $CP$ asymmetries between $D\to K^{+}{K}^{-}$ and $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 $D\to \ddot{I}€\ddot{I}€$. These results unambiguously imply a very large penguin contribution, having a central value $4.74$ times the magnitude of the amplitude for $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$. This fitted central value differs from a reasonable SM estimate of $10\%$ with a significance greater than $3.3\ddot{I}ƒ$. In contrast to previous studies, we present model-independent arguments based only on unitarity of re-scattering amplitudes to show that large penguins cannot arise from re-scattering 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.

8 pages, 10 figures; Version to be published in Phys. Rev. D

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