Coulomb Interaction in Ultrarare Leptonic Decays of B-Mesons

In this paper we present a method to account for the Coulomb interaction in the ultrarare lepton decays $$B_{{s,d}}^{0} \to {{\ell }^{ + }}{{\ell }^{ - }}$$ . Consideration of the Coulomb interaction for the decay of $$B_{s}^{0} \to {{\mu }^{ + }}{{\mu }^{ - }}$$ reduces the discrepancy between theory and experiment more than twice. The key idea of the paper is to change the procedure of secondary quantization—instead of expansion by plane waves, the solution of the Dirac equation in an external field (Furry picture) is used. The applicability of the Farry picture is justified on the example of the decay of a hypothetical neutral pseudoscalar particle into two charged scalars $${{B}^{0}} \to {{S}^{ + }}{{S}^{ - }}$$ .