<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>ℓ</mml:mo><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:

In this work, nontrivial analytic structure of the quark propagator is discussed for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi></a:mrow></a:math>-meson inclusive decays. Attributed to invalidity of the standard Källén-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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>B</c:mi><c:mo stretchy="false">→</c:mo><c:msub><c:mi>X</c:mi><c:mi>c</c:mi></c:msub><c:mo>ℓ</c:mo><c:mover accent="true"><c:mi>ν</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> decay as well as the lifetime of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msubsup><h:mi>B</h:mi><h:mi>d</h:mi><h:mn>0</h:mn></h:msubsup></h:math> meson are discussed. In the presence of the mentioned nonanalytical contributions, the possibility for resolving the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mo stretchy="false">|</j:mo><j:msub><j:mi>V</j:mi><j:mrow><j:mi>c</j:mi><j:mi>b</j:mi></j:mrow></j:msub><j:mo stretchy="false">|</j:mo></j:math> puzzle is addressed. It is demonstrated that there exists a parameter region, which explains <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mo stretchy="false">|</n:mo><n:msub><n:mi>V</n:mi><n:mrow><n:mi>c</n:mi><n:mi>b</n:mi></n:mrow></n:msub><n:mo stretchy="false">|</n:mo></n:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi>B</r:mi><r:mi>d</r:mi><r:mn>0</r:mn></r:msubsup></r:math>-meson lifetime simultaneously within <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:mn>1</t:mn><t:mi>σ</t:mi></t:mrow></t:math> via the complex conjugate poles from a charm quark.