Effective Hamiltonian forB→Xse+e−beyond leading logarithms in the naive dimensional regularization and ’t Hooft–Veltman schemes

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Abstract

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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