# $SU(3)$ breaking effects in $B$ and $D$ meson lifetimes

**Authors:** Daniel King, Alexander Lenz, Thomas Rauh  
**arXiv:** [2112.03691](https://arxiv.org/abs/2112.03691)  
**Date:** 2021-12-07  
**Summary page:** https://www.summarizepaper.com/en/paper/2112.03691v1/

## Key points

- Authors focus on non-perturbative matrix elements of four quark operators
- First determination of the effects of strange quark mass on dimension six matrix elements
- Calculation of eye contractions and penguin operators for the first time
- Solving 3-loop contribution to sum rule and evaluating condensate contributions
- Strict adherence to HQET limit in study
- Results can be used to estimate size of Darwin operator matrix element using equations of motion
- Contributes insights into $SU(3)$ breaking effects in $B$ and $D$ meson lifetimes

## Summary

The authors focus on non-perturbative matrix elements of four quark operators that arise as phase space enhanced contributions in this expansion. They provide the first determination of the effects of strange quark mass ($m_s$) on the dimension six matrix elements of these four quark operators through a heavy quark effective theory (HQET) sum rule analysis. Additionally, they calculate eye contractions of the four quark operators and matrix elements of penguin operators for the first time. To account for the perturbative part, they solve the 3-loop contribution to the sum rule and evaluate condensate contributions in their calculations. It is important to note that their study strictly adheres to the HQET limit. The results obtained from this analysis can be utilized to estimate the size of the matrix element of the Darwin operator using equations of motion. This study contributes valuable insights into understanding $SU(3)$ breaking effects in $B$ and $D$ meson lifetimes by investigating non-perturbative matrix elements and providing novel calculations for various quark operators.