Abstract
Theoretical predictions for t overline{t} b overline{b} production are of crucial importance for t overline{t} H measurements in the H → b overline{b} channel at the LHC. To address the large uncertainties associated with the modelling of extra QCD radiation in t overline{t} b overline{b} events, in this paper we present a calculation of pp → t overline{t} b overline{b} 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} b overline{b} 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} b overline{b} generators. Moreover, as we will argue, pp → t overline{t} b overline{b} j at NLO entails information that can be used to gain insights into the perturbative convergence of the inclusive t overline{t} b overline{b} cross section beyond NLO. Based on this idea, we address the issue of the large NLO K-factor observed in {sigma}_{toverline{t}boverline{b}} , and we provide evidence that supports the reduction of this K-factor through a mild adjustment of the QCD scales that are conventionally used for this process. The presented 2 → 5 NLO calculations have been carried out using OpenLoops 2 in combination with Sherpa and Munich.
Highlights
At leading order (LO) in QCD, the ttbb cross section is proportional to αS4 and suffers from huge scale uncertainties
We propose the idea of aligning dynamic scales to a natural scale, which can be defined using the maxima of the Next-to-leading order (NLO) variation curves as a reference
The most significant shape effects show up in the case of top-quark observables, where scale uncertainties can shift the level of the recoil peak by 15–20%, while for b-jets the flatness of the azimuthal correlations is remarkably stable with respect to higher-order effects. These results demonstrate that fixed-order NLO predictions for pp → ttbbj can be used as a precision benchmark to validate the modelling of recoil effects in Monte Carlo simulations of ttbb production
Summary
We investigate NLO QCD corrections to hadronic ttbbj production in the 4F scheme, i.e. we treat top quarks, and bottom quarks with a finite mass throughout. The independent partonic channels contributing to pp → ttbbj at NLO are summarised in table 1 together with the number of Feynman diagrams and crossing/flavour symmetries. At NLO in QCD, as usually the process receives contributions both from virtual and real corrections, which are separately divergent. To mediate these divergences between the different phase spaces, we rely on the dipole-subtraction formalism [26] in its extension to massive QCD partons [27]. In figure 2 (second row) we depict sample diagrams for the dominant all-gluon channel
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