Local duality and nonleptonic B decay

In the large $N_c$ limit, the nonleptonic width of the B meson is determined by the lepton mass spectrum in semileptonic B decay and the hadron mass spectrum in $\tau$ decay. This result can be compared with the nonleptonic width computed using the operator product expansion and local duality, to estimate the violation of local duality in B decay. In the absence of the required data, we use experimental Monte Carlo predictions and find that the difference is small, at the few percent level. We estimate the theoretical uncertainty in our results from higher order corrections (including $1\mathrm{/}{N}_c$ effects). We also identify a new contribution to the ${\mathrm{\Lambda }}_b-B$ lifetime difference.