### Speaker

Mr
Ilija Milutin
(University of Siegen)

### Description

The Heavy Quark Expansion has become the major tool for precision calculations for inclusive heavy hadron decays. The HQE is an expansion in $1/m_b$. Recently, moments of the dilepton spectrum of inclusive $B\to X_c\ell\bar{\nu}$ were used to precisely extract the CKM matrix element $V_{cb}$. Usually, one assumes that the charm quark is heavy, leading to $\Lambda_{\rm{QCD}}^n/m_c^n$-contributions. A consistent power counting therefore needs to be set up. Numerically, we find that $m_c^2\sim m_b\Lambda_{\rm{QCD}}$. Therefore, $m_c^2$ should be counted as one power of $m_b$. Consequently, we need to include $1/m_b^3\cdot1/m_c^2$-contributions to complete the existing calculation at $\mathcal{O}(1/m_b^4)$, which we will present here.

### Primary authors

Mr
Ilija Milutin
(University of Siegen)
Keri Vos
(University of Maastricht)
Thomas Mannel
(Siegen University)