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We study the rare leptonic decays $B_{s,d}^0 \to \ell^+\ell^-$ within thegeneral framework of the aligned two-Higgs doublet model. A complete one-loopcalculation of the relevant short-distance Wilson coefficients is presented,with a detailed technical summary of the results. The phenomenologicalconstraints imposed by present data on the model parameters are alsoinvestigated.

$B_{s,d}^0 \to \ell^+\ell^-$ Decays in Two-Higgs Doublet Models