Three-loop QCD corrections to B_s -> mu^+ mu^-

Understand

The decay B_s -> mu^+ mu^- 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 Q_A at low energies.

• We compute QCD corrections of order alpha_s^2 to its Wilson coefficient C_A.
• It requires performing three-loop matching between the full and effective theories.
• Including the new corrections makes C_A more stable with respect to the matching scale mu_0 at which the top-quark mass and alpha_s are renormalized.