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We report on the construction of a factorization theorem for the contributionof the electromagnetic dipole operator ${\cal O}_7$ to the $\bar B_s \to\mu^+\mu^-$ decay amplitude. The leading-order contribution from a QED boxdiagram features a double-logarithmic enhancement associated to the differentrapidities of the light quark in the $\bar B_s$-meson and the energetic muonsin the final state. We analyse the cancellation of the related endpointdivergences appearing in individual momentum regions, and show how the rapiditylogarithms can be isolated by suitable subtractions applied to thecorresponding bare factorization theorem. This allows us to include in astraightforward manner the QCD corrections arising from therenormalization-group running of the hard matching coefficient, thehard-collinear scattering kernel, and the $\bar B_s$-meson distributionamplitude.

Refactorization of endpoint divergencies for the ${\cal O}_7$ contribution to $\bar B_s \to \mu^+\mu^-$