Modeling top-quark decays in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">¯</mml:mo> <

We compare the fixed-order NLO QCD predictions for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>p</a:mi> <a:mi>p</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>t</a:mi> <a:mover accent="true"> <a:mi>t</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mi>t</a:mi> <a:mover accent="true"> <a:mi>t</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mo>+</a:mo> <a:mi>X</a:mi> </a:math> process in the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mn>4</h:mn> <h:mo>ℓ</h:mo> </h:math> decay channel with the parton-shower-based results obtained with the owheg and @ matching methods. In the first case, NLO QCD corrections are consistently included in both the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>t</j:mi> <j:mover accent="true"> <j:mi>t</j:mi> <j:mo stretchy="false">¯</j:mo> </j:mover> <j:mi>t</j:mi> <j:mover accent="true"> <j:mi>t</j:mi> <j:mo stretchy="false">¯</j:mo> </j:mover> </j:math> production step and the decays of the four top quarks, preserving all spin correlations. In the second approach, higher-order effects in top-quark decays with approximate spin correlations are simulated in the ythia parton-shower framework. Additionally, we analyze the impact of including the so-called matrix element corrections in top-quark decays in both parton-shower matched predictions. The comparison is performed at the integrated and differential fiducial cross-section level for the LHC center-of-mass energy of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msqrt> <p:mi>s</p:mi> </p:msqrt> <p:mo>=</p:mo> <p:mn>13.6</p:mn> <p:mtext> </p:mtext> <p:mtext> </p:mtext> <p:mi>TeV</p:mi> </p:math> .