NLO QCD predictions for t$$ \overline{t} $$b$$ \overline{b} $$ production in association with a light jet at the LHC

A bstract Theoretical predictions for t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> production are of crucial importance for t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> H measurements in the H → b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> channel at the LHC. To address the large uncertainties associated with the modelling of extra QCD radiation in t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> events, in this paper we present a calculation of pp → t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> j at NLO QCD. The behaviour of NLO corrections is analysed in a variety of observables, and to assess theoretical uncertainties we use factor- two rescalings as well as different dynamic scales. In this context, we propose a systematic alignment of dynamic scales that makes it possible to disentangle normalisation and shape uncertainties in a transparent way. Scale uncertainties at NLO are typically at the level of 20–30% in integrated cross sections, and below 10% for the shapes of distributions. The kinematics of QCD radiation is investigated in detail, including the effects of its recoil on the objects of the t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> system. In particular, we discuss various azimuthal correlations that allow one to characterise the QCD recoil pattern in a precise and transparent way. In general, the calculation at hand provides a variety of precise benchmarks that can be used to validate the modelling of QCD radiation in t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> generators. Moreover, as we will argue, pp → t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> j at NLO entails information that can be used to gain insights into the perturbative convergence of the inclusive t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> cross section beyond NLO. Based on this idea, we address the issue of the large NLO K -factor observed in $$ {\sigma}_{t\overline{t}b\overline{b}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯<

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