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

TL;DR

This paper investigates the effects of $SU(3)$ flavor symmetry breaking on $B$ and $D$ meson lifetimes by calculating non-perturbative matrix elements using HQET sum rules, including $m_s$ effects and eye contractions.

Contribution

First determination of $m_s$ effects on four-quark operator matrix elements in HQET sum rules, including eye contractions and penguin operators, in the strict HQET limit.

Findings

Calculated $m_s$ effects on matrix elements

Evaluated eye contractions and penguin operator contributions

Solved 3-loop perturbative sum rule contributions

Abstract

In the heavy quark expansion (HQE) of the total decay rates of $B_s$ and $D_s^+$ mesons non-perturbative matrix elements of four quark operators are arising as phase space enhanced contributions. We present the first determination of $m_s$ effects to the dimension six matrix elements of these four quark operators via a heavy quark effective theory (HQET) sum rule analysis. In addition we calculate for the first time eye contractions of the four quark operators as well as matrix elements of penguin operators. For the perturbative part we solve the 3-loop contribution to the sum rule and we evaluate condensate contributions. In this study we work in the strict HQET limit and our results can also be used to estimate the size of the matrix element of the Darwin operator via equations of motion.