QCD corrections for subleading powers in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow><

We compute next-to-leading order QCD corrections to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>1</a:mn><a:mo>/</a:mo><a:msubsup><a:mi>m</a:mi><a:mi>b</a:mi><a:mn>2</a:mn></a:msubsup></a:math> terms of the heavy quark expansion, for the contribution to inclusive nonleptonic bottom hadron decays, induced by the charged-current operators mediating the <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:mi>c</c:mi><c:mover accent="true"><c:mi>c</c:mi><c:mo stretchy="false">¯</c:mo></c:mover><c:mi>s</c:mi></c:math> transition. Their contributions to the lifetimes are Cabibbo favored and have large Wilson coefficients, but they have not been computed before, since the presence of two heavy quarks in the final state makes this calculation technically demanding. This work adds the last missing piece of the full NLO terms at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>1</h:mn><h:mo>/</h:mo><h:msubsup><h:mi>m</h:mi><h:mi>b</h:mi><h:mn>2</h:mn></h:msubsup></h:math> in the heavy quark expansion of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>B</j:mi></j:math>-hadron lifetimes. We obtain analytical results with full dependence on the final-state charm quark mass.