Inclusive Decays of Bottom Hadrons in New Formulation of Heavy Quark Effective Field Theory

TL;DR

This paper applies a new formulation of heavy quark effective field theory to inclusive bottom hadron decays, clarifying long-standing ambiguities and enabling precise extraction of CKM matrix elements, with results aligning well with experimental data.

Contribution

The paper introduces a new formulation of HQEFT that removes $1/m_b$ corrections and calculates $1/m_b^2$ contributions, improving the theoretical understanding of bottom hadron decays.

Findings

Lifetime ratios match experimental data

CKM element |V_cb| can be reliably extracted

Decay observables are consistent with measurements

Abstract

We apply the new formulation of heavy quark effective field theory (HQEFT) to the inclusive decays of bottom hadrons. The long-term ambiguity of using heavy quark mass or heavy hadron mass for inclusive decays is clarified within the framework of the new formulation of HQEFT. The $1/m_b$ order corrections are absent and contributions from $1/m_b^2$ terms are calculated in detail. This enables us to reliably extract the important CKM matrix element $|V_{cb}|$ from the inclusive semileptonic decay rates. The resulting lifetime ratios $\tau(B^0_s)/\tau(B^0)$ and $\tau(\Lambda_b)/\tau(B^0)$ are found to well agree with the experimental data. We also calculate in detail the inclusive semileptonic branching ratios and the ratios of the $\tau$ and $\beta$ decay rates as well as the charm countings in the $B^0$, $B^0_s$ and $\Lambda_b$ systems. For $B^0$ decays, all the observables are found to be consistent with the experimental data. More precise data for the $B^0$ decays and further experimental measurements for the $B^0_s$ and $\Lambda_b$ systems will be very useful for testing the framework of new formulation of HQEFT at the level of higher order corrections.