Third order correction to semileptonic $b\to u$ decay: fermionic contributions

Abstract

We present the QCD corrections of order ${\alpha }_s^3$ to the decay rate of $b\to u\ell {\bar{\nu }}_{\ell }$, with $\ell =e,\mu$, originating from diagrams with closed fermion loops and neglecting the mass of the up quark. Our calculation relies on integration-by-parts reduction of Feynman integrals with one propagator raised to a symbolic power in Kira and the numerical evaluation of master integrals with AMFlow. This allows us to obtain results for the fermionic contributions to the total semileptonic rate with an accuracy of more than thirty digits.

5 pages, 2 figures. v2: references added, matches published version

References in corpus (12)

• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Precision determination of the CKM element Vcb
• Mass effects in muon and semileptonic b -> c decays
• Inclusive semileptonic B decays and the determination of |V_ub|
• Three loop calculations and inclusive $V_{cb}$
• Heavy-to-heavy quark decays at NNLO
• Inclusive Measure of |V_ub| with the Analytic Coupling Model
• Massive vector form factors to three loops
• Normalizing inclusive rare B decays
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• Three-loop corrections to the muon and heavy quark decay rates
• Massive three-loop form factors: anomaly contribution