Dipenguin - like contributions to D 0 − D̄ 0 mixing

We show that because of the milder GIM suppression, the four-quark dipenguin operator contributes to the short distance piece of the D − D̄ mixing amplitude at the same order of magnitude as the box diagram. In addition, we put an upper bound ∆m D ≤ 5 ×∆mbox D on a long-distance resonant contribution induced by the penguin mixing. The phenomenon of meson mixing has been studied for a long time. Observed in the K − K̄0 and B − B̄0 systems, it provides an extremely sensitive test of the Standard Model (SM). Extremely large value of the top quark mass makes the short distance box diagram (e.g. Fig.1a) dominate B − B̄0 and K − K̄0 mixing amplitudes. This fact effectively turns GIM cancellation mechanism (vanishing of the total ∆Q = 2 contribution in the limit of equal internal quark masses) into the ”GIM-enhancement” of the short-distance contribution to ∆mP for P = {K,B}. Long-distance contributions associated with the propagation of the hadronic degrees of freedom and higher-order QCD effects are relatively unimportant for the mixing of B and K mesons. The situation is drastically different in the case of the D − D̄0 system: the only available heavy b-quark contribution to the box diagram providing ∆C = 2 transition is greatly reduced by a tiny Vub CKM matrix element and can be safely neglected in the analysis of the box diagram contribution to ∆mD (the inclusion of the b-quark further decreases the box diagram contribution [1]). This forces the vanishing of the effect in the SU(3) limit and implies that only the light quark mass difference guarantees that mixing does take place. Calculating a box diagram and constructing the effective Hamiltonian, we realize that the smallness of the short distance piece is guaranteed by a factor of (ms − md)/mc [2] (we define L = (1 + γ5)/2) Heff = GF 2π2 ξsξd (ms −md) mc [ ūγμLcūγμLc+ 2 ūRcūRc ]