Speaker
Description
In this talk, I will present progress on the computation of the leptonic $B^- \rightarrow \ell^- \bar{\nu}_\ell$ decay in SCET. Above the confinement scale $\Lambda_{\rm QCD}$, we describe the virtual QED corrections of the decay with an EFT construction based on $\text{SCET}_{\rm I}\otimes \text{HQET}$ where both hard collinear and collinear modes are treated as independent degrees of freedom. Matching this theory to $\text{SCET}_{\rm II}\otimes \text{HQET}$, we refactorize the end-point divergent contribution and derive the order $\mathcal{O}(\alpha)$ contributions of the decay amplitude involving two- and three-particles Light-cone distribution amplitudes (LCDAs) of the B meson. We derive a factorization theorem for virtual corrections at the amplitude level and express virtual corrections in an effective Yukawa coupling. Below $\Lambda_{\rm QCD}$, we match the partonic picture to a low-energy EFT based on a combination of heavy meson EFT (HMET) and boosted heavy lepton EFT (bHELT). We demonstrate that, depending on the cut on final state radiation and on the lepton flavor, the real emission contribution from excited states of the B meson can become important and must be included in the low-energy EFT description.