Can FCNC transition c → ul + l − be seen in D → V l + l − decays?

The decays D → V l + l − present in principle the opportunity to observe the short distance FCNC transition c → ul + l − , which is sensitive to the physics beyond the Standard Model. We analyze the D → V l + l − decays within the Standard Model, where in addition to the short distance dynamics also the long distance dynamics is present. The short distance contribution due to c → ul + l − transition, which is present only in the Cabibbo suppressed decays, is found to be three orders of magnitude smaller than the long distance contribution. The branching ratios well above 10 −7 for Cabibbo suppressed decays could signal new physics. The most frequent decays are the Cabibbo allowed decays D + s → ρ + µ + µ − and D 0 → ¯ K * 0 µ + µ − , which are expected at the branching ratios of 3 · 10 −5 and 1.7 · 10 −6 , respectively. These rates are not much lower than the present experimental upper limit. In the charm sector the phenomena like D 0 − ¯ D 0 mixing, CP-violation and rare decay probabilities are small, which makes them good candidates as probes for New physics with small background from the Standard Model. The smallness of the short-distance (SD) c → ul + l − rate within the Standard Model suggests that the decays D → V l + l − (V is light vector meson) could serve as a possible good window to non-standard contributions to the flavour-changing neutral transition c → ul + l − [1,2]. We analyse all D → V l + l − decays within the Standard Model, where except for the short distance dynamics also the long distance (LD) dynamics is present. We calculate the SD and LD contributions using the hybrid model, which combines heavy quark and chiral perturbation theory. The SD contribution due to c → ul + l − is present only in the Cabibbo suppressed decays D −. In this decays our motivation is to determine the relative magnitude of SD and LD contribution. Our results should provide the appropriate theoretical background against which possible signals of new physics are searched for. Motivated by the experimental searches, we analyze also the Cabibbo allowed decays (D 0 → K * 0 l + l …