We present the Mathematica application "LieART" (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.

Abstract:We compute the hadronic production of top-antitop pairs in association with a Higgs boson at next-to-leading-order QCD, including the decay of the top and antitop quark into bottom quarks and leptons. Our computation is based on full leading and next-to-leading-order matrix elements for e + ν e µ −ν µ bbH(j) and includes all non-resonant contributions, off-shell effects and interferences. Numerical results for the integrated cross section and several differential distributions are given for the LHC operating at 13 TeV using a fixed and a dynamical factorization and renormalization scale. The use of the dynamical instead of the fixed scale improves the perturbative stability in high-energy tails of most distributions, while the integrated cross section is hardly affected differing by only about one per cent and leading to almost the same K factor of about 1.17.

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We present the Mathematica application "LieART" (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.

We present an analysis of Higgs-boson production in association with a topquark pair at the LHC investigating in particular the final state consisting of four b jets, two jets, one identified charged lepton and missing energy. We consider the Standard Model prediction in three scenarios, the resonant Higgs-boson plus top-quark-pair production, the resonant production of a top-quark pair in association with a b-jet pair and the full process including all non-resonant and interference contributions. By comparing these scenarios we examine the irreducible background for the production rate and several kinematical distributions. With standard selection criteria the irreducible background turns out to be three times as large as the signal. For most observables we find a uniform deviation of eight percent between the scenario requiring two resonant top quarks and the full process. In particular phase-space regions the non-resonant contributions cause larger effects, and we observe shape changes for some distributions. Furthermore we investigate interference effects and find that neglecting interference contributions results in an over-estimate of the total cross-section of five percent.