A Vademecum on Quark-Hadron Duality

Abstract

We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the Small Velocity expansion. A new potentially significant mechanism for violation of local duality in Γ_sl(B) is analyzed. Yet we conclude that the amount of duality violation in Γ_sl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. Violation of local duality in Γ_sl(B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B->D^* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark-hadron duality than Γ_sl(B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of V_cb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark-hadron duality in semileptonic B->X_c lνdecays.