On the four-quark operator matrix elements for the lifetime of $\Lambda_{b}$

TL;DR

This paper uses full QCD sum rules to evaluate four-quark operator matrix elements affecting the lifetime of the $ ext{Lambda}_b$, aiming to reduce uncertainties in heavy quark expansion predictions.

Contribution

It introduces a novel application of full QCD sum rules to compute four-quark operator matrix elements for $ ext{Lambda}_b$, addressing a key source of uncertainty.

Findings

First-time calculation of four-quark matrix elements using full QCD sum rules.

Consideration of contributions from up to dimension-6 operators.

Potential to resolve the $ ext{Omega}_c$ lifetime puzzle.

Abstract

Heavy quark expansion can nicely explain the lifetime of $\Lambda_{b}$. However, there still exist sizable uncertainties from the four-quark operator matrix elements of $\Lambda_{b}$ in $1/m_{b}^{3}$ corrections, which describe the spectator effects. In this work, these four-quark operator matrix elements are investigated using full QCD sum rules for the first time. At the QCD level, contributions from up to dimension-6 four-quark operators are considered. Our method of calculating high-dimensional operator matrix elements is promising to be used to resolve the $\Omega_{c}$ lifetime puzzle.