Three-loop QCD corrections to Bs → μ+μ -

Abstract

The decay Bs → μ+μ- in the Standard Model is generated by the well-known W-box and Z-penguin diagrams that give rise to an effective quark-lepton operator QA at low energies. We compute QCD corrections of order αs2 to its Wilson coefficient CA. It requires performing three-loop matching between the full and effective theories. Including the new corrections makes CA more stable with respect to the matching scale μ0 at which the top-quark mass and αs are renormalized. The corresponding uncertainty in |CA|2 gets reduced from around 1.8% to less than 0.2%. Our results are directly applicable to all the Bs(d) → ℓ+ℓ- decay modes.