Inclusive B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ with a hadronic mass cut

Abstract The hadronic mass spectrum of inclusive B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ is investigated at next to leading order in the heavy quark expansion. For mild cuts on the hadronic mass, the expansion, which applies when the cut is released, remains convergent. However, the cuts used at BaBar and Belle to reduce backgrounds from charged current semileptonic processes are too severe for a description in terms of matrix elements of local operators to apply. Strategies for interpolating between the two regions are discussed.