Calculation of 1/mc3terms in the total semileptonic width ofDmesons

We calculate the 1/${\mathit{m}}_{\mathit{c}}^3$ corrections in the inclusive semileptonic widths of D mesons. We show that these are due to the novel penguin-type operators that appear at this level in the transition operator. Taking into account the nonperturbative corrections leads to the predicted value of the semileptonic width significantly lower than the experimental value. The 1/${\mathit{m}}_{\mathit{c}}^3$ corrections worsen the situation or, at the very least, within uncertainty, give a small contribution. We indicate possible ways out of this problem. It seems most probable that violations of duality are noticeable in the energy range characteristic to the inclusive decays in the charm family. Theoretically these deviations are related to divergence of the high-order terms in the power expansion in the inverse heavy quark mass.