Heavy-to-light currents at NNLO in SCET and semi-inclusive B¯→Xsℓ+ℓ− decay

We perform the two-loop matching calculation for heavy-to-light currents from QCD onto soft-collinear effective theory for the complete set of Dirac structures. The newly obtained matching coefficients enter several phenomenological applications, of which we discuss heavy-to-light form factor ratios and exclusive radiative decays, as well as the semi-inclusive decay B¯→Xsℓ+ℓ−. For this decay, we observe a significant shift of the forward–backward asymmetry zero and find q02=(3.34−0.25+0.22)GeV2 for an invariant mass cut mXcut=2.0GeV.