Speaker
Description
(Part of the CRC project C1b)
In this talk, I plan to discuss the current status of theory predictions for lifetimes of heavy $H = B, D$-mesons (containing a heavy quark $Q = b,c$), which can be presented schematically within the Heavy Quark Expansion (HQE) framework as:
$$
\Gamma(H) =
\Gamma_3 +
\Gamma_5 \frac{\langle {\cal O}_5 \rangle}{m_Q^2} +
\Gamma_6 \frac{\langle {\cal O}_6 \rangle}{m_Q^3} + ...
+ 16 \pi^2
\left[
\tilde{\Gamma}_6 \frac{\langle \tilde{\mathcal{O}}_6 \rangle}{m_Q^3}
+ \tilde{\Gamma}_7 \frac{\langle \tilde{\mathcal{O}}_7 \rangle}{m_Q^4} + ...
\right],
$$
where ${\cal O}_d$ denotes the effective operator of dimension $d$, with the matrix element $ \langle {\cal O}_d \rangle \equiv \langle H | {\cal O}_d | H \rangle$, and $\Gamma_d$ is the corresponding short-distance Wilson coefficient. Then I will discuss more in detail the recent first determination of Darwin operator contribution $\Gamma_6$. In addition, I will present some results on the phenomenology, and will discuss further prospects and plans on improvement of the HQE predictions for these lifetimes - both from perturvative and non-perturbative side - by the Siegen and Karlsruhe Universities.
