I present a calculation of approximate N$^3$LO 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 aN$^3$LO results for the total $t{\bar t}$ cross section,
the top-quark $p_T$ and rapidity distributions, and the top-quark
forward-backward asymmetry. The higher-order corrections are significant and
they reduce theoretical uncertainties.Comment: 6 pages, 5 figures; presented at the XXIII International Workshop on
  Deep-Inelastic Scattering and Related Subjects, Dallas, Texas, 27 April - 1
  May 2015; to appear in PoS(DIS2015

Kidonakis, Nikolaos

English

arXiv

I present a calculation of approximate N3LO 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 aN3LO results for the total tt¯ cross section, the top-quark pT and rapidity distributions, and the top-quark forward-backward asymmetry. The higher-order corrections are significant and they reduce theoretical uncertainties

DigitalCommons@Kennesaw State University

Kennesaw State UniversityDigitalCommons@Kennesaw State UniversityFaculty Publications5-1-2015N3LO Approximate Results for Top-quarkDifferential Cross Sections and Forward-backwardAsymmetryNikolaos KidonakisKennesaw State University, nkidonak@kennesaw.eduFollow this and additional works at: https://digitalcommons.kennesaw.edu/facpubsPart of the Physics CommonsThis Article is brought to you for free and open access by DigitalCommons@Kennesaw State University. It has been accepted for inclusion in FacultyPublications by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please contactdigitalcommons@kennesaw.edu.Recommended CitationKidonakis, Nikolaos, "N3LO Approximate Results for Top-quark Differential Cross Sections and Forward-backward Asymmetry"(2015). Faculty Publications. 3848.https://digitalcommons.kennesaw.edu/facpubs/3848arXiv:1506.04068v1  [hep-ph]  12 Jun 2015 N3LO approximate results for top-quark differentialcross sections and forward-backward asymmetryNikolaos Kidonakis∗†Department of Physics, Kennesaw State University, Kennesaw, GA 30144, USAE-mail: nkidonak@kennesaw.eduI present a calculation of approximate N3LO corrections from NNLL soft-gluon resummation fordifferential distributions in top-antitop pair production in hadronic collisions. Soft-gluon correc-tions are the dominant contribution to top-quark production and closely approximate exact resultsthrough NNLO. I show aN3LO results for the total t ¯t cross section, the top-quark pT and rapiditydistributions, and the top-quark forward-backward asymmetry. The higher-order corrections aresignificant and they reduce theoretical uncertainties.XXIII International Workshop on Deep-Inelastic Scattering27 April - May 1 2015Dallas, Texas∗Speaker.†This material is based upon work supported by the National Science Foundation under Grant No. PHY 1212472.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/N3LO approximate results for top-quark differential cross sections ... Nikolaos Kidonakis6 7 8 9 10 11 12 13 14S1/2 (TeV)1001000σ (pb)aN3LO centralaN3LO +- scaleaN3LO +-scale&pdfLHC combo  7 TeVLHC combo  8 TeVpp -> tt    at  LHC  energies      aN3LO7 8150200250165 170 175 180mt (GeV)5678910σ (pb)aN3LONNLOCDF & D0 combopp -> tt   at  Tevatron      cross section +- scale      S1/2=1.96 TeV Figure 1: Total aN3LO cross sections for t ¯t production at the LHC (left) and the Tevatron (right) andcomparison with LHC [7, 8] and Tevatron [9] data.1. IntroductionThe calculation of higher-order corrections for t ¯t total cross sections, top-quark transversemomentum (pT ) and rapidity distributions, and the top forward-backward asymmetry (AFB) is animportant part of top-quark physics. QCD corrections are very significant for top-antitop pair pro-duction. Soft-gluon corrections, calculated appropriately, are the dominant part of these correctionsat LHC and Tevatron energies. The soft corrections are currently known through N3LO [1–3].The soft-gluon terms in the nth-order perturbative corrections involve [lnk(s4/m2t )]/s4 withk≤ 2n−1 and s4 the kinematical distance from partonic threshold. We resum these soft correctionsat 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-spaceresummation in perturbative QCD. The first N3LO expansion was given in [5] with a completeformal expression given in [6]. Approximate N3LO (aN3LO) total and differential cross sectionsfrom the expansion of the NNLL resummed expressions have been obtained most recently in [1,2]. The latest aN3LO results for the total cross section [1], top pT and rapidity distributions [2],and the top forward-backward asymmetry AFB [3], provide the best and state-of-the-art theoreticalpredictions.It has been known for some time that the partonic threshold approximation in our formalismworks very well for LHC and Tevatron energies; the differences between approximate and exactcross sections at both NLO and NNLO are at the per mille level. This is also true for pT and rapiditydistributions and AFB. The use of a fixed-order expansion removes the need for a prescription todeal with divergences and the unphysical effects of such prescriptions. The stability and robustnessof the theoretical higher-order results in our resummation approach over the past two decades aswell 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 TevatronIn Fig. 1 we show the aN3LO total t ¯t cross sections at LHC and Tevatron energies [1] and2N3LO approximate results for top-quark differential cross sections ... Nikolaos Kidonakis0 50 100 150 200 250 300 350 400pT (GeV)00.0020.0040.0060.0081/σ  dσ/dp T (GeV-1 )aN3LOscale variation+ CMSNormalized top pT distribution at the LHC      S1/2=7 TeV 200 300 40010-410-30 50 100 150 200 250 300 350 400pT (GeV)00.0020.0040.0060.0081/σ  dσ/dp T (GeV-1 )aN3LOscale variation+ ATLAS l+jetsNormalized top pT distribution at the LHC      S1/2=7 TeV 400 600 80010-510-410-3Figure 2: Normalized aN3LO top-quark pT distributions at the 7 TeV LHC, and comparison with CMSdata [11] in the dilepton (black) and lepton+jets (red) channels (left plot), and with ATLAS data [12] in thelepton+jets channel (right plot).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 at1.96 TeV energy [9]. We use MSTW2008 NNLO pdf [10] for all our predictions. The agreementof theoretical predictions with experimental data is excellent.We also provide the aN3LO total t ¯t cross sections with mt = 173.3 GeV below. At the Tevatronwith 1.96 TeV energy the cross section is 7.37+0.09−0.27+0.38−0.28 pb; at the 7 TeV LHC it is 174+5−7+9−10 pb;at the 8 TeV LHC it is 248+7−8+12−13 pb; at the 13 TeV LHC it is 810+24−16+30−32 pb; and at the 14 TeVLHC it is 957+28−19+34−36 pb. The first uncertainty in the previous numbers is from scale variation overmt/2≤ µ ≤ 2mt and the second is from the MSTW2008 pdf [10] at 90% C.L.Fractional contributions to the perturbative series for the t ¯t cross section at the LHC convergewell through N3LO, which could potentially indicate that corrections beyond N3LO are negligible[1]. For Tevatron energies the convergence is slower [1].3. Top-quark pT and rapidity distributions at the LHC and the TevatronIn Fig. 2 we show the normalized aN3LO top-quark pT distribution, (1/σ)dσ/d pT , at 7 TeVLHC energy and compare with results from CMS in the dilepton and lepton+jets channels [11] andfrom ATLAS in the lepton+jets channel [12]. We find excellent agreement between the theoreticalresults and the 7 TeV LHC data. The theoretical predictions are also in excellent agreement withrecent CMS top pT data at 8 TeV in both channels [13].In the left plot of Fig. 3 we show the aN3LO top-quark pT distributions [2], dσ/d pT , at 13 and14 TeV LHC energies. In the right plot of Fig. 3 we show the aN3LO top-quark pT 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 aN3LO top-quark rapidity distribution, (1/σ)dσ/dY , at 7 TeV LHCenergy and compare with results from CMS in the dilepton and lepton+jets channels [11], findingexcellent agreement between theory and data. The theoretical predictions at 8 TeV are also in3N3LO approximate results for top-quark differential cross sections ... Nikolaos Kidonakis0 50 100 150 200 250 300pT (GeV)01234567dσ/dp T (pb/GeV)aN3LO  14 TeVaN3LO  13 TeVaNNLOTop quark pT distribution at LHC     aN3LO mt=173.3 GeV     µ=mt/2, mt, 2mt0 50 100 150 200 250 300 350 400pT (GeV)00.020.040.060.08dσ/dp T (pb/GeV)aN3LOscale variation+ D0Top quark pT distribution  Tevatron  S1/2=1.96 TeV  mt=172.5 GeV   200 250 300 350 40010-410-310-2Figure 3: Top-quark aN3LO pT distributions at the LHC (left) and at the Tevatron compared to D0 data [14](right).-3 -2 -1 0 1 2 3Y00.10.20.30.41/σ  dσ/dYaN3LOscale variation+ CMSNormalized top rapidity distribution at LHC   S1/2=7 TeV-3 -2 -1 0 1 2 3Y050100150200250300dσ/dY (pb)aN3LO  14 TeVaN3LO  13 TeVaNNLOTop quark rapidity distribution at  LHC      aN3LOmt=173.3 GeV     µ=mt/2, mt, 2mtFigure 4: (Left) Top-quark aN3LO normalized rapidity distributions at the 7 TeV LHC and comparison withCMS data [11] in the dilepton (black) and lepton+jets (red) channels; (Right) Top-quark aN3LO rapiditydistributions at 13 and 14 TeV LHC energies.excellent agreement with recent CMS top rapidity data in both channels [13]. We also show theaN3LO top-quark rapidity distributions, dσ/dY , at 13 and 14 TeV LHC energies in the right plotof Fig. 4.In the left plot of Fig. 5 we compare the aN3LO distribution of the absolute value of thetop-quark rapidity, dσ/d|Y |, at the Tevatron with D0 data [14] and find very good agreement.4. Top-quark forward-backward asymmetry at the TevatronFinally, we discuss the top forward-backward asymmetry at the TevatronAFB =σ(yt > 0)−σ(yt < 0)σ(yt > 0)+σ(yt < 0). (4.1)4N3LO approximate results for top-quark differential cross sections ... Nikolaos Kidonakis0 0.5 1 1.5 2|Y|0246810dσ/d|Y| (pb)aN3LOscale variation+ D0Top quark rapidity at Tevatron   S1/2=1.96 TeV   m=172.5 GeV   0 0.5 1 1.5 2|∆y|00.10.20.30.40.50.6AFBCDFD0aN3LOAFB at Tevatron   S1/2=1.96 TeV   mt=173.3 GeV   Figure 5: (Left) Top-quark aN3LO dσ/d|Y | distribution at the Tevatron compared with D0 data [14]; (Right)Top-quark aN3LO differential AFB at the Tevatron compared with CDF [16] and D0 [17] data.The above expression can be evaluated with numerator and denominator separately at fixed-orderor it can be re-expanded in αs (see [3] for details through aN3LO). As was discussed in [3] thesoft-gluon corrections are dominant and in our formalism they precisely predicted [15] the exactasymmetry at NNLO. The high-order perturbative corrections are large: the aN3LO/NNLO ratio is1.08 without re-expansion in αs, or 1.05 with re-expansion in αs. Including electroweak correctionsand the aN3LO QCD corrections we find an asymmetry of (10.0±0.6)% in the t ¯t frame using re-expansion in αs.The differential top forward-backward asymmetry is defined byAbinFB =σ+bin(∆y)−σ−bin(∆y)σ+bin(∆y)+σ−bin(∆y)with ∆y = yt − y¯t .In the right plot of Fig. 5 we plot the differential AFB and compare with recent results fromCDF [16] and D0 [17]. The agreement between theory and experiment is very good for both thetotal and the differential asymmetries.5. SummaryThe N3LO soft-gluon corrections for top-antitop pair production are significant and providethe best available theoretical predictions. Results have been presented for the total t ¯t cross sections,the top-quark pT and rapidity distributions, and the top-quark forward-backward asymmetry. Thecorrections are large at LHC and Tevatron energies and they reduce the theoretical uncertaintiesfrom scale variation. There is excellent agreement between aN3LO theoretical predictions andLHC and Tevatron data.References[1] N. Kidonakis, NNNLO soft-gluon corrections for the top-antitop pair production cross section, Phys.Rev. D 90, 014006 (2014) [arXiv:1405.7046 [hep-ph]].5N3LO approximate results for top-quark differential cross sections ... Nikolaos Kidonakis[2] N. Kidonakis, NNNLO soft-gluon corrections for the top-quark pT and rapidity distributions, Phys.Rev. D 91, 031501(R) (2015) [arXiv:1411.2633 [hep-ph]].[3] N. Kidonakis, The top quark forward-backward asymmetry at approximate N3LO, Phys. Rev. D 91,071502(R) (2015) [arXiv:1501.01581 [hep-ph]].[4] N. Kidonakis, Next-to-next-to-leading soft-gluon corrections for the top quark cross section andtransverse momentum distribution, Phys. Rev. D 82, 114030 (2010) [arXiv:1009.4935 [hep-ph]].[5] N. Kidonakis, High-order corrections and subleading logarithms for top quark production, Phys. Rev.D 64, 014009 (2001) [hep-ph/0010002].[6] N. Kidonakis, Next-to-next-to-next-to-leading-order soft-gluon corrections in hard-scatteringprocesses near threshold, Phys. Rev. D 73, 034001 (2006) [hep-ph/0509079].[7] ATLAS and CMS Collaborations, Combination of ATLAS and CMS top-quark pair cross-sectionmeasurements using proton-proton collisions at√s = 7 TeV, ATLAS-CONF-2012-134, CMS PASTOP-12-003.[8] ATLAS and CMS Collaborations, Combination of ATLAS and CMS top quark pair cross sectionmeasurements in the eµ final state using proton-proton collisions at √s = 8 TeV,ATLAS-CONF-2014-054, CMS PAS TOP-14-016.[9] CDF and D0 collaborations, Combination of measurements of the top-quark pair production crosssection from the Tevatron Collider, Phys. Rev. D 89, 072001 (2014) [arXiv:1309.7570[hep-ex]].[10] A.D. Martin, W.J. Stirling, R.S. Thorne, and G. Watt, Parton distributions for the LHC, Eur. Phys. J.C 63, 189 (2009) [arXiv:0901.0002 [hep-ph]].[11] CMS Collaboration, Measurement of differential top-quark pair production cross sections in ppcolisions at√s = 7 TeV, Eur. Phys. J. C 73, 2339 (2013) [arXiv:1211.2220 [hep-ex]].[12] ATLAS Collaboration, Measurements of normalized differential cross sections for t ¯t production in ppcollisions at√s = 7 TeV using the ATLAS detector, Phys. Rev. D 90, 072004 (2014) [arXiv:1407.0371[hep-ex]].[13] CMS Collaboration, Measurement of the differential cross section for top quark pair production in ppcollisions at√s = 8 TeV, arXiv:1505.04480 [hep-ex].[14] D0 Collaboration, Measurement of differential t ¯t production cross sections in pp¯ collisions, Phys. Rev.D 90, 092006 (2014) [arXiv:1401.5785 [hep-ex]].[15] N. Kidonakis, The top quark rapidity distribution and forward-backward asymmetry, Phys. Rev. D 84,011504(R) (2011) [arXiv:1105.5167 [hep-ph]].[16] CDF Collaboration, Measurement of the top quark forward-backward production asymmetry and itsdependence on event kinematic properties, Phys. Rev. D 87, 092002 (2013) [arXiv:1211.1003[hep-ex]].[17] D0 Collaboration, Measurement of the forward-backward asymmetry in top quark-antiquarkproduction in pp¯ collisions using the lepton+jets channel, Phys. Rev. D 90, 072011 (2014)[arXiv:1405.0421 [hep-ex]].6

N3LO Approximate Results for Top-quark Differential Cross Sections and Forward-backward Asymmetry

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N$^3$LO approximate results for top-quark differential cross sections
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N $^3$ LO approximate results for top-quark differential cross sections and forward-backward asymmetry

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N3^33LO approximate results for top-quark differential cross sections and forward-backward asymmetry

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N $^3$ LO approximate results for top-quark differential cross sections and forward-backward asymmetry