Searching for the origin of CP violation in Cabibbo-suppressed D-meson decays

The recent evidence of relatively large direct CP violation in D-0 decay at LHCb suggests that CP studies in the D system may become an important new avenue for understanding CP just as studies in the B system have proven to be. The current level of CP violation could be consistent with the Standard Model or, perhaps, contain evidence of new physics. A clean Standard Model prediction of the CP violation in these decays would, of course, be important in understanding these results but hadronic uncertainties make such a prediction difficult. In this paper, we make several suggestions to try to seek the role of new physics. We propose that the hadronic enhancement needed to attribute the observed CP violation in D to two pseudoscalar modes may not operate for inclusive final states, where it is likely that we will see asymmetries at the quark level expectation provided the source is the Standard Model. A simple way to implement this is to search for CP asymmetries in final states containing K and (K) over bar but where the sum of their energies is less than the energy of the parent D. This is meant to ensure that the event belongs to an inclusive and not an exclusive sample. We also propose that CP asymmetries may be enhanced in modes where the tree is color suppressed. In particular, the final state rho(0)rho(0) is of special interest because it consists of charged pions only and, in addition, it can have C-even P-odd triple product correlations; similarly, D-s -> rho K-0(+) and rho K-0*(+) also appear interesting. We also emphasize the use of CPT constraints leading to interesting correlations. We then consider how isospin symmetry can provide observables that are sensitive to certain classes of new physics and are small in the Standard Model. In particular, we discuss using isospin analysis in the decays D -> pi pi, rho pi, and rho rho as well as in D-s -> K*pi. We also consider how such analysis may eventually be supplemented by information about the weak phases in D-0 decay. In order to obtain this information experimentally, we consider various methods for preparing an initial state that is a quantum mechanical mixture of D-0 and (D) over bar (0). This may be done through the use of natural D-0/(D) over bar (0) oscillations; observing D-0 mesons that arise from B-d or B-s mesons, which themselves are oscillating, or from quantum correlations in D-0 pairs that arise from either psi '' decay or B-meson decay. Observing CP violation in the magnitudes of decay amplitudes should be within the capability of experiments in the near future; however, obtaining the weak phases through the methods we discuss will likely require future generations of machines due to the large statistics that are likely to be needed.