Effective Hamiltonian for<i>B</i>→<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">X</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>beyond leading logarithms in the naive dimensional regularization and ’t Hooft–Veltman schemes

We calculate the next-to-leading QCD corrections to the effective Hamiltonian for B\ensuremath{\rightarrow}${\mathit{X}}_{\mathit{s}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ in the NDR and tHV schemes. We give for the first time analytic expressions for the Wilson coefficient of the operator ${\mathit{Q}}_{9}$=(s\ifmmode\bar\else\textasciimacron\fi{}b${)}_{\mathit{V}\mathrm{\ensuremath{-}}\mathit{A}}$(e\ifmmode\bar\else\textasciimacron\fi{}e${)}_{\mathit{V}}$ in the NDR and HV schemes. Calculating the relevant matrix elements of local operators in the spectator model we demonstrate the scheme independence of the resulting short-distance contribution to the physical amplitude. Keeping consistently only leading and next-to-leading terms, we find an analytic formula for the differential dilepton invariant mass distribution in the spectator model. A numerical analysis of the ${\mathit{m}}_{\mathit{t}}$, ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{MS}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}$, and \ensuremath{\mu}=O(${\mathit{m}}_{\mathit{b}}$) dependences of this formula is presented. We compare our results with those given in the literature.

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