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

TL;DR

This paper calculates third-order QCD corrections to the semileptonic decay rate of b to u quarks, focusing on fermionic loop contributions, using advanced integral reduction and numerical methods for high precision.

Contribution

It provides the first detailed computation of fermionic contributions at order ^3 to becay, employing novel numerical techniques for high-precision results.

Findings

Fermionic contributions to decay rate computed with over thirty digits accuracy.

First calculation of third-order fermionic corrections for becay.

Results enhance precision in theoretical predictions of semileptonic decay rates.

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.