Is right-handed current contribution to $\bar{B}\to X_{u}l\nu$ decays corrected by non-trivial vacuum in QCD?

We study violation of quark-hadron duality for $\bar{B}\to X_{u}l\nu$ and $D\to X_{d}l\nu$ decays in the presence of the right-handed current operator. For this case, we show that duality violation has some aspects different from the standard model due to the existence of an instanton. In particular, the fermionic zero mode of an intermediate light quark can give a nonvanishing contribution owing to its chirality structure. A duality-violating component that arises from a single instanton is then analytically extracted as a finite-distance singularity, leading to an oscillatory correction to the observable in Minkowski space. Finally, we show that the size of duality violation for the lepton energy distribution in $\bar{B}$ decays can be comparable to the chirally suppressed perturbative contribution although the absolute size depends on the detail of the QCD vacuum.