# Top Pair Production With a Jet With
Nlo Qcd

Off-Shell Effects ^{1}^{1}1Presented at the
Rencontres de Moriond session devoted to QCD and High Energy
Interactions, La Thuile, 19-26 March 2016. ^{2}^{2}2Preprint
number:
TTK-16-15.

\abstracts
A brief summary of the recent next-to-leading order QCD calculation for at the LHC is given. Our computation includes all non-resonant contributions, off-shell effects and interferences for top-quarks and gauge bosons. Some results for integrated and differential cross sections are shown for the LHC Run1 energy of 8 TeV. A significant reduction of the scale dependence is observed, which indicates that the perturbative expansion is well under control. The results are obtained in the framework of the Helac-Nlo system.

Since its discovery at the Tevatron till the collider’s shut-down in 2011, the properties of the top quark and its interactions have been studied in detail at the center-of-mass energy of TeV. These studies are now continued at the LHC, which is in operation since the end of 2009. Starting from Run1 energies, i.e. TeV and continuing with Run2 energy of TeV many aspects of the top quark physics have been examined very precisely. Theoretical predictions have also been significantly improved recently. By now full calculations for the total inclusive cross section exist [1] along with the level predictions for various differential distributions [2, 3]. The synergy between the very precise theoretical predictions and the LHC data allowed to improve our knowledge of the strong coupling constant and the top-quark mass, which are both crucial parameters of the SM. Moreover, theoretical predictions helped to constrain the gluon parton distribution functions at large , that are crucial when calculating any cross sections in collisions. Besides its tremendous role in improving our understanding of QCD and the electroweak theory, the top quark plays an important role in many scenarios for new physics beyond the SM, which constitutes one of the main motivation for the top quark physics program at the LHC. Precise predictions for the cross section helped to constrain BSM physics either by putting new stringent limits on various new physics scenarios or by proposing new ideas to improve search methods. The large collision energy and luminosity of the LHC, result in top quarks being produced in very large quantities. Consequently, they are produced with large energies and high transverse momenta, which increases the probability for additional (hard) jet radiation and result in more exclusive final states like for example production. In order to improve our knowledge of the inclusive cross section such an exclusive final state must be well under control. The first question that can arise is about the size of the contribution to the inclusive sample. For a cut of GeV almost of events are actually accompanied by an additional hard jet. A good understanding of the process is, thus, a prerequisite for a more precise understanding of the topology of top-quark events. However, the process is also interesting by itself. It constitutes the dominant background process to the Higgs boson production in the vector boson fusion with Higgs boson decays into . Typical vector boson cuts for two tagging (hardest in ) jets, denoted by , consist of and . When comparing rapidity distributions of the hardest light- and b-jet for two production processes and it is clearly visible that -jets are produced centrally while light-jets are distributed more evenly (see Figure 1). Asking for two tagging (b-) jets to fulfil such requirements in case of will dramatically decrease the contribution from the process. On the other hand, for the process in presence of the additional light-jet it is sufficient that only one -jet is considered to be the tagging jet. As a consequence, not the inclusive production, but is the dominant background process for . In addition, production plays a very important role in searches for physics beyond the SM. With +jet and final states is the main background to processes such as supersymmetric particle production, where depending on the specific model, typical signals include jets, charged leptons, and missing due to the escaping lightest supersymmetric particle.

Owing to the importance of production we calculate NLO QCD corrections for this process including all non-resonant diagrams, interferences, and off-shell effects of top-quarks and gauge bosons [4]. In practice corrections are evaluated to the following LO process at . Representative LO Feynman diagrams are shown in Figure 2. For the inclusive cross section contributions from top quark off-shell effects are formally suppressed by the top-quark width () [5, 6, 7, 8]. They can, however, be strongly enhanced for more exclusive observables [9]. Here, NLO QCD corrections have been calculated with the Helac-Nlo Monte Carlo program [10]. The virtual corrections have been obtained with Helac-1Loop [11] and CutTools [12], which are based on the Ossola-Papadopoulos-Pittau reduction technique [13]. The OneLOop program [14] has been used for the evaluation of the scalar integrals. The process under consideration requires a special treatment of unstable top-quarks, which is achieved within the complex mass scheme. The singularities from soft or collinear parton emissions are isolated via subtraction methods for NLO QCD calculations that are implemented in Helac-Dipoles [15]. Specifically, two independent subtraction schemes have been employed: the commonly used Catani-Seymour dipole subtraction [16, 17], and a fairly new Nagy-Soper subtraction scheme [18]. The phase space integration was performed with the multichannel Monte Carlo generator Kaleu [19].

In the following we present selected results for at the LHC with TeV. The SM parameters and cuts are specified below

where stands for and for the light- or -jet. Jets are defined by the anti- jet algorithm with the separation parameter and MSTW2008 parton distribution functions are chosen. Results for the total cross sections are as follows

(1) |

The full cross section receives negative and moderate NLO corrections of at the central scale, i.e. for . Theoretical uncertainties, associated with neglected higher order terms in the perturbative expansion, have been estimated to be at LO and at NLO. Thus, a reduction of the theoretical error by a factor of 3 was observed. We have also assessed the size of the non-factorizable corrections. At LO (NLO) finite top-quark width effects changed the cross section by less than . Representative differential distributions are presented in Figure 3, where we exhibit the transverse momentum of the hardest (in ) light jet and the separation between charged leptons in the rapidity azimuthal angle plane. The dashed (blue) curve corresponds to the LO, whereas the solid (red) one to the NLO result. The upper panels show the distributions themselves and the scale dependence bands. The lower panels display the differential factor. Higher order corrections to do not simply rescale the shape of the LO distribution. Corrections up to are introduced away from the threshold for the production. Thus, the differential cross section can only be properly described when the higher order corrections are taken into account. A judicious choice of the dynamic scale, could, however, change negative NLO corrections in the high tails and a constant factor could be achieved in the whole region. On the contrary, for the distribution, negative, moderate and quite stable corrections have been observed, because receives contributions from all scales, most notably from those that are sensitive to the threshold for the production. Indeed, for our scale choice, effects of the phase space regions close to this threshold dominate and a dynamic scale will not alter the behaviour in that case.

To summarise, we have calculated NLO QCD corrections to with complete off-shell and interference effects both for top-quarks and gauge bosons. We have shown that NLO QCD corrections to the total cross section are moderate but their impact on some differential distributions is much larger. We have also estimated the size of the top quark off-shell effects at NLO for the total cross section, and confirmed that they are of the order of . Let us stress here, that process can add to alternative methods of determination of the top-quark mass. One method recently proposed involves the invariant mass of the system [20, 21]. However, to extract the top-quark mass as precisely as possible the most complex calculation for need to be considered that consists of a full simulation of the final state without any approximations. Thus, in the next step our results can be used to extract the top-quark pole mass with a very high precision.

The author would like to thank the organizers of Recontres de Moriond for the kind invitation and the very pleasant atmosphere during the conference. The work was supported by the DFG under Grant: ”Signals and Backgrounds Beyond Leading Order. Phenomenological studies for the LHC”.

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