Completing $1/m_b^3$ corrections to non-leptonic bottom-to-up-quark decays

TL;DR

This paper calculates specific higher-order corrections to the decay rates of heavy hadrons involving bottom-to-up-quark transitions, providing analytical expressions for key terms in the heavy quark expansion.

Contribution

It introduces the computation of $1/m_b^3$ corrections from dimension six operators, specifically for non-leptonic bottom-to-up-quark decays, with explicit analytical formulas.

Findings

Derived analytical expressions for $ ho_D$ and $ ho_{LS}$ terms.

Enhanced understanding of decay width contributions at higher order.

Provides tools for more precise predictions of heavy hadron decays.

Abstract

We compute the contributions of dimension six two-quark operators to the non-leptonic decay width of heavy hadrons due to the flavor changing bottom-to-up-quark transition in the heavy quark expansion. Analytical expressions for the Darwin term $\rho_D$ and the spin-orbit term $\rho_{\rm LS}$ are obtained with leading order accuracy.