# High-precision theory for top-quark production

###### Abstract

I present high-precision results for top quark production at hadron collider energies. Total and differential cross sections are calculated through aNLO for top-antitop pair production and through aNNLO for single-top production. Top production in association with a charged Higgs boson and via anomalous couplings is also briefly discussed.

High-precision theory for top-quark production

Nikolaos Kidonakis^{†}^{†}thanks: Speaker. ^{†}^{†}thanks: This material is based upon work supported by the National Science Foundation under Grant No. PHY 1519606.

Department of Physics, Kennesaw State University, Kennesaw, GA 30144, USA

E-mail: nkidonak@kennesaw.edu

\abstract@cs

## 1 Introduction

The top quark is the heaviest elementary particle ever discovered and thus holds a very special place in the list of fundamental particles. It is predominantly produced in hadron colliders via top-antitop pair production processes and to a lesser extent via single-top production channels (for recent reviews see [1, 2]). Associated top production with a charged Higgs boson and top production via anomalous couplings are also of interest.

The QCD corrections to top production processes are typically quite large and need to be included for precise predictions. At current collider energies these corrections are dominated by soft-gluon emission. Thus one can derive excellent approximations to high-order corrections by calculating soft-gluon corrections. Such corrections need to be calculated through NLO to achieve percent-level or better precision.

In this paper we present high-precision theoretical results for top quark total and differential cross sections in various processes, including top-antitop pair production [3, 4, 5] in Section 2, single-top production [6, 7, 8, 9, 10] in Section 3, top production in association with a charged Higgs boson [11] in Section 4, and top production via anomalous couplings [12] in Section 5.

## 2 Top-antitop pair production

The QCD corrections for production are quite large. Fixed-order NNLO calculations are now available based on a variety of analytical and numerical approaches by many groups (see [2, 13] for reviews). Soft-gluon corrections are dominant [3, 4, 5] and they approximate the exact results very well at both NLO and NNLO.

We can calculate/resum these soft corrections at NNLL accuracy. Various approaches have been proposed over the years (see [13] for a review) and there are big differences in the accuracies of the various approximations. The method we use here has been the most successful in predicting the NNLO results, and the calculations of additional soft-gluon NLO corrections from NNLL resummation provide the best theoretical predictions for the production cross sections and differential distributions [3, 4, 5].

Approximate NLO (aNLO) predictions for the cross section are derived by adding the third-order soft-gluon corrections to the fixed-order results:

aNLO = LO + NLO + NNLO + soft-gluon NLO corrections

### 2.1 Top-antitop pair aNLO cross sections at the LHC and the Tevatron

In Fig. 1 we plot the aNLO [3] total cross section with theoretical uncertainties at Tevatron and LHC energies and compare with recent data. The left plot shows results for the cross section at 1.96 Tevatron energy as a function of top quark mass while the plot on the right shows the cross section as a function of LHC energy. The agreement between data and the aNLO predictions is excellent in all cases.

The aNLO total cross section with GeV and MSTW2008 NNLO pdf [14] takes the value of pb at 13 LHC energy, where the first uncertainty is from scale variation and the second is the pdf uncertainty at 90% CL.

### 2.2 Relative size of the perturbative corrections

The relative sizes of the higher-order corrections and the convergence of the perturbative series are of course of great interest. We write the perturbative series through third order in the strong coupling as

(2.0) |

where is the LO cross section, and are respectively the complete NLO and NNLO corrections, and are the aNLO corrections.

corrections | Tevatron 1.96 TeV | LHC 7 TeV | LHC 8 TeV | LHC 13 TeV | LHC 14 TeV |
---|---|---|---|---|---|

0.236 | 0.470 | 0.476 | 0.493 | 0.496 | |

0.106 | 0.178 | 0.177 | 0.172 | 0.170 | |

0.068 | 0.066 | 0.059 | 0.045 | 0.043 | |

1.410 | 1.714 | 1.712 | 1.710 | 1.709 |

In Table 1 we show the values of the ratios of the higher-order corrections to the LO cross section as well as the ratio - in the last line - of the total aNLO cross section to the LO cross section. It is clear that higher-order corrections are very sizable for total cross sections, and this also holds for differential distributions. It is also obvious that NNLO is not enough! The aNLO corrections are clearly needed for precision physics.

### 2.3 Top-quark aNLo distributions at the LHC

In Fig. 2 we plot the aNLO [4] top-quark normalized transverse-momentum, , distribution with scale variation at 7 TeV LHC energy and compare with CMS data in the dilepton and lepton+jet channels, finding very good agreement in both cases. The inset plots highlight the large- region.

### 2.4 Top-quark aNLO rapidity distributions at the LHC

In Fig. 4 we plot the aNLO [4] top-quark normalized rapidity distribution at 7 TeV LHC energy and compare with CMS data in the dilepton and lepton+jet channels, finding excellent agreement between theory and data in both channels.

### 2.5 Top-quark aNLo and rapidity distributions and at the Tevatron

In the left plot of Fig. 6 we plot the aNLO [4] top-quark distribution with scale variation at 1.96 TeV Tevatron energy and find very good agreement with D0 data.

The top forward-backward asymmetry at the Tevatron, , takes the aNLO [5] QCD value -including EW corrections- of % in the frame. We note that the corrections are large: the aNLO/NNLO ratio is 1.05.

## 3 Single-top production

We continue with single-top production which can proceed through -channel processes, and ; -channel processes, ; and associated production, .

The aNNLO single-top cross sections as functions of LHC energy are shown in Fig. 7. As can be clearly seen, there is excellent agreement of theory [6, 7, 8] with data for all three channels.

### 3.1 Single-top -channel production at aNNLO

The aNNLO [8] single-top and single-antitop -channel cross sections at the current 13 TeV LHC energy with GeV are, respectively, and pb. The errors indicated are from scale variation and pdf uncertainties from the MSTW2008 NNLO pdf at 90% CL.

The aNNLO [9, 10] top and antitop distributions in the channel at 7, 8, 13, and 14 TeV LHC energies are shown in Fig. 8.

Some -channel aNNLO normalized distributions at 8 and 13 TeV energies at the LHC are shown in Fig. 9 and compared with CMS data.

### 3.2 Single-top -channel production at aNNLO

The aNNLO [6] single-top and single-antitop -channel cross sections at the current 13 TeV LHC energy with GeV are, respectively, and pb.

### 3.3 production at aNNLO

The aNNLO [7] cross section at the current 13 TeV LHC energy with GeV is pb. The cross section for is the same.

## 4 production at aNNLO

We next present aNNLO [11] results for charged Higgs production in association with a top quark at LHC energies, using MMHT2014 NNLO pdf [41].

In Fig. 12 we plot the aNNLO [11] cross sections at various LHC energies as functions of the charged Higgs mass, and also the associated factors at 13 TeV energy.

## 5 Top production via anomalous couplings

Single-top production may proceed via anomalous couplings in theories beyond the Standard Model. Soft-gluon corrections for top production via anomalous gluon couplings were calculated through aNNLO in [12]. For processes via anomalous -- couplings, the soft-gluon corrections are significant in enhancing the cross section and reducing the scale dependence.

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