-- Main.HamishGordon - 21 Aug 2008

  • S. Bianco, F. L. Fabbri, D. Benson and I. Bigi, Riv. Nuovo Cim. 26N7-8, 1 (2003).

In singly Cabibbo-suppressed modes, on the other hand, there are two amplitudes driven by c → ddu and c → s ̄u, respectively. As explained before the leading term in ̄the penguin diagram here represents a nonlocal operator, since the internal s quark in the loop is lighter than the external charm quark. The [penguin] not only has a different weak phase than the [tree], but—being a one-loop diagram with internal quarks s, d being lighter than the c quark—induces also a strong phase. One cannot rely, though, on this diagram to obtain a quantitative prediction. This penguin diagram with ms,d < mc does not represent a local operator and cannot reliably be treated by short-distance dynamics. Searching for direct CP violation in Cabibbo-suppressed D decays as a sign for New Physics would however represent a very complex challenge: the CKM benchmark men- tioned above points to asymmetries of order 0.1%. One can perform an analysis like in ref. [381] based on theoretical engineering of hadronic matrix elements and their phase shifts as described above. There one typically finds asymmetries ∼ O(10−4 ), i.e. some- what smaller than the rough benchmark stated above. Yet 10−3 effects are conceivable, and even 1% effects cannot be ruled out completely. Observing a CP asymmetry in charm decays would certainly be a first rate discovery even irrespective of its theoretical inter- pretation. Yet to make a case that a signal in a singly Cabibbo-suppressed mode reveals New Physics is quite iffy. In all likelihood one has to analyze at least several channels with comparable sensitivity to acquire a measure of confidence in one’s interpretation.

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