Effective Hamiltonian for B→${\mathit{X}}_{\mathit{s}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ 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→${\mathit{X}}_{\mathit{s}}$ ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ 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¯b${)}_{\mathit{V}\mathrm{-}\mathit{A}}$(e¯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 ${\mathit{m}}_{\mathit{t}}$, ${\mathrm{\Lambda }}_{\mathrm{MS}\mathrm{¯}}$, and μ=O(${\mathit{m}}_{\mathit{b}}$) dependences of this formula is presented. We compare our results with those given in the literature.