# NLO approximate results for top-quark differential cross sections and forward-backward asymmetry

###### Abstract

I present a calculation of approximate NLO corrections from NNLL soft-gluon resummation for differential distributions in top-antitop pair production in hadronic collisions. Soft-gluon corrections are the dominant contribution to top-quark production and closely approximate exact results through NNLO. I show aNLO results for the total cross section, the top-quark and rapidity distributions, and the top-quark forward-backward asymmetry. The higher-order corrections are significant and they reduce theoretical uncertainties.

NLO approximate results for top-quark differential cross sections and forward-backward asymmetry

Nikolaos Kidonakis^{†}^{†}thanks: Speaker. ^{†}^{†}thanks: This material is based upon work supported by the National Science Foundation under Grant No. PHY 1212472.

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

E-mail: nkidonak@kennesaw.edu

\abstract@cs

## 1 Introduction

The calculation of higher-order corrections for total cross sections, top-quark transverse momentum () and rapidity distributions, and the top forward-backward asymmetry () is an important part of top-quark physics. QCD corrections are very significant for top-antitop pair production. Soft-gluon corrections, calculated appropriately, are the dominant part of these corrections at LHC and Tevatron energies. The soft corrections are currently known through NLO [1, 2, 3].

The soft-gluon terms in the th-order perturbative corrections involve with and the kinematical distance from partonic threshold. We resum these soft corrections at NNLL accuracy via factorization and renormalization-group evolution of soft-gluon functions [4]. The calculation is for the double-differential cross section using the standard moment-space resummation in perturbative QCD. The first NLO expansion was given in [5] with a complete formal expression given in [6]. Approximate NLO (aNLO) total and differential cross sections from the expansion of the NNLL resummed expressions have been obtained most recently in [1, 2]. The latest aNLO results for the total cross section [1], top and rapidity distributions [2], and the top forward-backward asymmetry [3], provide the best and state-of-the-art theoretical predictions.

It has been known for some time that the partonic threshold approximation in our formalism works very well for LHC and Tevatron energies; the differences between approximate and exact cross sections at both NLO and NNLO are at the per mille level. This is also true for and rapidity distributions and . The use of a fixed-order expansion removes the need for a prescription to deal with divergences and the unphysical effects of such prescriptions. The stability and robustness of the theoretical higher-order results in our resummation approach over the past two decades as well as the correct prediction of the size of the exact NNLO corrections validate our formalism.

## 2 Top-antitop pair total cross sections at the LHC and the Tevatron

In Fig. 1 we show the aNLO total cross sections at LHC and Tevatron energies [1] and compare them with LHC combination data from the ATLAS and CMS collaborations at 7 TeV [7] and 8 TeV [8] energies, and Tevatron combination data from the CDF and D0 collaborations at 1.96 TeV energy [9]. We use MSTW2008 NNLO pdf [10] for all our predictions. The agreement of theoretical predictions with experimental data is excellent.

We also provide the aNLO total cross sections with GeV below. At the Tevatron with 1.96 TeV energy the cross section is pb; at the 7 TeV LHC it is pb; at the 8 TeV LHC it is pb; at the 13 TeV LHC it is pb; and at the 14 TeV LHC it is pb. The first uncertainty in the previous numbers is from scale variation over and the second is from the MSTW2008 pdf [10] at 90% C.L.

## 3 Top-quark and rapidity distributions at the LHC and the Tevatron

In Fig. 2 we show the normalized aNLO top-quark distribution, , at 7 TeV LHC energy and compare with results from CMS in the dilepton and lepton+jets channels [11] and from ATLAS in the lepton+jets channel [12]. We find excellent agreement between the theoretical results and the 7 TeV LHC data. The theoretical predictions are also in excellent agreement with recent CMS top data at 8 TeV in both channels [13].

In the left plot of Fig. 3 we show the aNLO top-quark distributions [2], , at 13 and 14 TeV LHC energies. In the right plot of Fig. 3 we show the aNLO top-quark distributions [2] at 1.96 TeV Tevatron energy and compare with D0 data [14], finding very good agreement.

We continue with the top-quark rapidity distribution at the LHC [2]. In the left plot of Fig. 4 we show the normalized aNLO top-quark rapidity distribution, , at 7 TeV LHC energy and compare with results from CMS in the dilepton and lepton+jets channels [11], finding excellent agreement between theory and data. The theoretical predictions at 8 TeV are also in excellent agreement with recent CMS top rapidity data in both channels [13]. We also show the aNLO top-quark rapidity distributions, , at 13 and 14 TeV LHC energies in the right plot of Fig. 4.

## 4 Top-quark forward-backward asymmetry at the Tevatron

Finally, we discuss the top forward-backward asymmetry at the Tevatron

(4.0) |

The above expression can be evaluated with numerator and denominator separately at fixed-order or it can be re-expanded in (see [3] for details through aNLO). As was discussed in [3] the soft-gluon corrections are dominant and in our formalism they precisely predicted [15] the exact asymmetry at NNLO. The high-order perturbative corrections are large: the aNLO/NNLO ratio is 1.08 without re-expansion in , or 1.05 with re-expansion in . Including electroweak corrections and the aNLO QCD corrections we find an asymmetry of ()% in the frame using re-expansion in .

The differential top forward-backward asymmetry is defined by

## 5 Summary

The NLO soft-gluon corrections for top-antitop pair production are significant and provide the best available theoretical predictions. Results have been presented for the total cross sections, the top-quark and rapidity distributions, and the top-quark forward-backward asymmetry. The corrections are large at LHC and Tevatron energies and they reduce the theoretical uncertainties from scale variation. There is excellent agreement between aNLO theoretical predictions and LHC and Tevatron data.

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