Three-loop QCD corrections to heavy-to-light form factors and applications to inclusive $B$ decays

Abstract

We report on the calculation of heavy-to-light form factors at $\mathcal{O}({\alpha }_s^3)$ and on selected phenomenological applications in inclusive $B$-decays. After outlining the loop calculation, we extract the hard function in $\bar{B}\to X_s\gamma$, and discuss our recent progress and preliminary results for the N${}^3$LO corrections to partial decay rates in $\bar{B}\to X_{u}l{\bar{\nu }}_l$, important for the inclusive determination of $|V_{ub}|$. In particular, we establish relations for heavy-quark parameters in the shape-function scheme to four loops and improve a particular model of the $B$ meson shape-function.

Comments: 13 pages, 2 figures; talk presented at Loops and Legs in Quantum Field Theory 2026