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

Understand

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.