Lifetimes and HQE

TL;DR

This paper reviews the Heavy Quark Expansion (HQE) theory for heavy hadron lifetimes, discusses recent experimental tests, and updates theoretical lifetime predictions, highlighting the role of non-perturbative matrix elements.

Contribution

It provides a pedagogic overview of HQE, reviews recent experimental validations, and updates lifetime predictions with current data and theoretical limitations.

Findings

HQE has passed several experimental tests with high precision.

Updated lifetime ratios for B and heavy baryons are provided.

The main theoretical limitation is the unknown size of non-perturbative matrix elements.

Abstract

Kolya Uraltsev was one of the inventors of the Heavy Quark Expansion (HQE), that describes inclusive weak decays of hadrons containing heavy quarks and in particular lifetimes. Besides giving a pedagogic introduction to the subject, we review the development and the current status of the HQE, which just recently passed several non-trivial experimental tests with an unprecedented precision. In view of many new experimental results for lifetimes of heavy hadrons, we also update several theory predictions: $\tau (B^+) / \tau (B_d) = 1.04^{+0.05}_{-0.01} \pm 0.02 \pm 0.01$, $\tau (B_s) / \tau (B_d) = 1.001 \pm 0.002$, $\tau (\Lambda_b)/ \tau (B_d) = 0.935 \pm 0.054$ and $\bar {\tau} (\Xi_b^0) / \bar{\tau} (\Xi_b^+) = 0.95 \pm 0.06$. The theoretical precision is currently strongly limited by the unknown size of the non-perturbative matrix elements of four-quark operators, which could be determined with lattice simulations.