On an exact low-energy duality in heavy-quark semileptonic decay

Abstract

Shifman and Voloshin have pointed out that in a certain limit there would be an exact and calculable duality between quark- and hadronic-level pictures of meson semileptonic decay. I show here that this duality is local in the Dalitz plot and correct to next-to-leading order in the heavy quarks' mass difference. I then discuss some implications of these results for extracting $V_{\mathrm{cb}}$ from data on $B\to \mathrm{De}{\overline{v}}_e$ and $D^{*}e{\overline{v}}_e$.