$B\to X_c\ell\bar{\nu}$ Decay as a Probe of Complex Conjugate Poles

In this work, nontrivial analytic structure of the quark propagator is discussed for $B$-meson inclusive decays. Attributed to invalidity of the standard K\"{a}ll\'{e}n-Lehman spectral representation, complex conjugate poles alter the evaluation of decay rates, which lead to violation of quark-hadron duality. As phenomenological observables, widths in $B\to X_c\ell\bar{\nu}$ decay as well as the lifetime of the $B_d^0$ meson are discussed. In the presence of the mentioned nonanalytical contributions, the possibility for resolving the $|V_{cb}|$ puzzle is addressed. It is demonstrated that there exists a parameter region, which explains $|V_{cb}|$ and $B_d^0$-meson lifetime simultaneously within 1$\sigma$ via the complex conjugate poles from a charm quark.