Charge Symmetry Breaking in $DD\to \alpha \pi ^0$ and $np\to D\pi ^0$

A. Fonseca (Lisbon), A. Gardestag (Indiana), C. Hanhart (Julich), C.J. Horowitz (Indiana), A. Nogga (Tuscon), G.A. Miller, U. van Kolck (Arizona)

As noted above the experimental paper observing the reaction $DD\to \alpha \pi ^0$ has been submitted to PRL[2], and I am a co-author. But the theorists task is to compute the cross section. First results for $\sigma(DD\to \alpha\pi^0)$ have been obtained for both in plane wave approximation and in including distortions. We have analyzed several reaction mechanisms. The important ones are the effects of external $\eta-\pi$ mixing[63], charge symmetry breaking in $\pi N$ scattering[64] (if the effect of distortions are included) and an enhancement of $\eta-\pi$ mixing via heavy meson exchange. We are in the process of analyzing the new IUCF data along with recently announced results for the $np\to D\pi ^0$ reaction[65]. Charge symmetry predicts that the $D$ and $\pi^0$ are emitted symmetrically about 90$^\circ$ in the center of mass. The effects of charge symmetry breaking in $\pi N$ scattering led to a correction prediction of the sign of the asymmetry[66], but the magnitude is not as large as we expected. So refinements of the calculation are necessary. The ultimate aim is to extract consistent values of the mass difference between the up and down quarks using a combined analysis of the two experiments. Various improvements of the theory are in progress[67].