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$\mathcal{O}(α_s^3)$ corrections to semileptonic $b \to c$ decays in the heavy daughter approximation

Kay Schoenwald

SciPost Phys. Proc. 7, 027 (2022) · published 21 June 2022

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We present our recent calculation of the third order corrections to the semileptonic $b \to c$ and the muon decays. The calculation has been performed in an expansion around the limit $m_c \sim m_b$, but shows decent convergence even for $m_c=0$ from which the contribution to the muon decay can be extracted. For the semileptonic $b \to c$ decay we find large perturbative corrections in the on-shell scheme which can be significantly reduced by changing to the kinetic scheme for the bottom quark mass. These results are important input for the inclusive determination of $|V_{cb}|$ and the Fermi coupling constant $G_F$.

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