Dynamical scales for multi-TeV top-pair production at the LHC

Journal of High Energy Physics, Apr 2017

We calculate all major differential distributions with stable top-quarks at the LHC. The calculation covers the multi-TeV range that will be explored during LHC Run II and beyond. Our results are in the form of high-quality binned distributions. We offer predictions based on three different parton distribution function (pdf) sets. In the near future we will make our results available also in the more flexible fastNLO format that allows fast re-computation with any other pdf set. In order to be able to extend our calculation into the multi-TeV range we have had to derive a set of dynamic scales. Such scales are selected based on the principle of fastest perturbative convergence applied to the differential and inclusive cross-section. Many observations from our study are likely to be applicable and useful to other precision processes at the LHC. With scale uncertainty now under good control, pdfs arise as the leading source of uncertainty for TeV top production. Based on our findings, true precision in the boosted regime will likely only be possible after new and improved pdf sets appear. We expect that LHC top-quark data will play an important role in this process.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP04%282017%29071.pdf

Dynamical scales for multi-TeV top-pair production at the LHC

Received: June Dynamical scales for multi-TeV top-pair production at Michal Czakon 0 1 3 David Heymes 0 1 2 Alexander Mitov 0 1 2 Cambridge 0 1 CB 0 1 HE U.K. 0 1 Based on our 0 1 Open Access 0 1 c The Authors. 0 1 0 exible fastNLO format that 1 Aachen , D-52056 Germany 2 Cavendish Laboratory, University of Cambridge 3 Institut fur Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University We calculate all major di erential distributions with stable top-quarks at the LHC. The calculation covers the multi-TeV range that will be explored during LHC Run II and beyond. Our results are in the form of high-quality binned distributions. We o er predictions based on three di erent parton distribution function (pdf) sets. In the near future we will make our results available also in the more allows fast re-computation with any other pdf set. In order to be able to extend our calculation into the multi-TeV range we have had to derive a set of dynamic scales. Such scales are selected based on the principle of fastest perturbative convergence applied to the di erential and inclusive cross-section. Many observations from our study are likely to be applicable and useful to other precision processes at the LHC. With scale uncertainty now under good control, pdfs arise as the leading source of uncertainty for TeV top production. QCD Phenomenology Contents 1 Introduction 2 3 4 Overview of past work related to scale setting Choosing the scale Total cross-section Di erential distributions Pdf related issues Phenomenological applications Introduction which is well-understood in (resummed) NNLO QCD [4{7]. metric mt and S uncertainties. Signi cantly, all these sources of error are comparable in contributors to tot are at the level of about 1% and include EW corrections, nite top width and various non-perturbative e ects. vetoes if pT;veto applicability to the total inclusive cross-section has been validated. The main goal of this paper is to identify the functional form of 0 . We choose such and factorisation scales, i.e. R;0 = F;0 = . Scale variation, however, is done independently for F and F;R 2 ( 0=2; 2 0) R= F sensible choice among possible dynamic scales has to be made. that o ers faster convergence is better. Clearly, the scale 0 will depend on the set of considered functional forms. production due to resummation of large collinear logs in this work. distributions and demonstrate that our \best" scales 0 are stable with respect to the Arxiv submission of this paper. Overview of past work related to scale setting has long history. Within such an approach factorisation and renormalisation scales are checks can be even quantitative. scales [38{41]. be found in ref. [52]. for an observable is renormalisation scheme independent to any nite order. In e ect, this higher order corrections, but not necessarily set them to zero. BLM/PMC and the usual scale setting approaches can be found in ref. [3]. Choosing the scale of functional forms: mT = HT = HT0 = ET = HT;int = (mt=2)2 + p2T;t + q (mt=2)2 + p2T;t ; the xing of the proportionality constant, signi ed by the sign in the above equations. pdf. The strong coupling constant S is evaluated through the LHAPDF interface [73] di erential distributions is performed by independently varying R (as de ned in use simultaneous F = R scale variation. Total cross-section mt=173.3 GeV mt=173.3 GeV scale F = Two important observations can be made from gure 1 and they turn out to be central for this work: rst, the scale for which perturbative convergence is maximised is slightly value of the xed order NNLO cross-section evaluated at the scale of fastest convergence small fraction of the scale uncertainty of the resummed result). positive higher order corrections. of fully inclusive top-pair production at the LHC. the inclusion of higher orders decreases the total cross-section. these two scales. The picture emerging from gure 1 has a direct analogue in inclusive Higgs production at larger values of indicates that the perturbative series is not converging well there and therefore such large scales should be avoided. F = R dependence of the total crossfunction of the scale is rather similar to the one with a xed scale. The only noticeable 4We only consider the gg ! h channel in the limit of large mt. 0 = (es -10 r (es -10 r mt=173.3 GeV mt=173.3 GeV R = Each plot is normalised as in gure 1, i.e. to the NNLO+NNLL cross-section evaluated with the distinguish the various lines. mt=173.3 GeV LO NLO NNLO mt=173.3 GeV gure 2 but for scale ET (3.5) (left) and HT0 (3.4) (right). Both use pdf set From gure 3 (left) we conclude that the numerical di erence between the two scales is (es -10 r NNLO QCD mt=173.3 GeV NNLO QCD mt=173.3 GeV bols on some of the lines are meant to help distinguish the various lines. = 0 8. We have not studied in depth this peculiar behaviour but point or at a minimum, may warrant similar investigations in other processes. for both pdf sets. From this gure it is easy to see that at this order of perturbation value = 0 = 1=2. Di erential distributions In determining the functional form of the scale 0 one is constrained by the following limiting cases: at pT ! 0 we have 0 The two constants c0 and c c0mt, while for very large pT we have 0 1 are a priori unknown as is the scale's functional form that 5We thank Bryan Webber for a helpful discussion on this point. constants c 1 and c0 should necessarily be equal. Indeed, the typical value used in the past for the former constant is c in the limits pT;t ! 0 and pT;t ! 1 thus arriving at the following \best" scale 0 = for: pT;t; pT;t and pT;t=t ; for: all other distributions : pdf sets: NNPDF3.0 [75], CT14 [78] and MMHT2014 [79]. ve di erent dynamic leads to K-factors that are closest to unity, i.e. it ts best the requirement for fastest b, is de ned: KNaLO=NbLO( ) = the scale choice at NNLO is rather limited. the smallest scale variation. The comparison in gure 6 demonstrates that mtt-based scales lead to poor perturbetween c0 = 1=2 and c1 = 1. Ratio to mT/2 (all in NNLO QCD) Ratio to mT/2 (all in NNLO QCD) mt=173.3 GeV mt=173.3 GeV pT,avt [GeV] pT,avt [GeV] Ratio to mT/2 (all in NNLO QCD) Ratio to mT/2 (all in NNLO QCD) mt=173.3 GeV mt=173.3 GeV pT,avt [GeV] pT,avt [GeV] from scale variation only. Pdf related issues dently of the pdf set. In 1.2 Ratio to HT/4 (all in NNLO QCD) 1.2 Ratio to HT/4 (all in NNLO QCD) ve di erent variation only. are not related to the choice of dynamic scale. To that end in gure 10 we show the pT;t=t NLO LO mt=173.3 GeV 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 mt=173.3 GeV mt=173.3 GeV mt=17t3t-.+3XG(e8VTeV) 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 mt=173.3 GeV 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 mt=173.3 GeV NLO LO 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 Figure 8. As in gure 7 but for the mtt distribution. mt=173.3 GeV 1000 1500 2000 2500 3000 3500 4000 2000 2500 3000 3500 4000 -mtt 1.2 PmtP=→17t3t-.+3XG(e8VTeV) Ratio to NNPDF30 (all in NNLO QCD) NLO mt=17t3t-.+3XG(e8VTeV) 200 400 600 800 1000 1200 1400 1600 1800 2000 2000 2500 3000 3500 4000 1.6 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 between di erential distributions and K-factors apparent from gures 7, 8, 9 are of pdf pdf sets.7 To further demonstrate this, in gure 11 we show the gg-luminosities for the three kindly providing us with these plots. 600 800 1000 1200 1400 1600 1800 2000 2500 3000 3500 4000 0.7 Ratio to NNPDF30 (NLO partonic; NNLO pdf) 0.8 Ratio to NNPDF30 (NLO partonic; NNLO pdf) 600 800 1000 1200 1400 1600 1800 2000 2500 3000 3500 4000 0.7 Ratio to NNPDF30 (LO partonic; NNLO pdf) 0.8 Ratio to NNPDF30 (LO partonic; NNLO pdf) 200 400 600 800 1000 1200 1400 1600 1800 2000 2500 3000 3500 4000 0.8 Ratio to NNPDF30 (NNLO partonic; NNLO pdf) 200 400 600 800 1000 1200 1400 1600 1800 2000 1.6 A5l0l0with 1N0NL0O0pdf1500 2000 2500 3000 3500 4000 0.7 Ratio to NNPDF30 (NNLO partonic; NNLO pdf) 1000 1500 2000 2500 3000 3500 4000 similar to the ones in gures 5, 6 and most importantly, the K-factors for the \best" scale all dynamic scales considered by us. Phenomenological applications NNLO with three di erent pdf sets: NNPDF3.0, MMHT2014 and CT14.8 narrow enough so they might be combined to t the usually much wider experimental theoretical analysis. results for all seven F;R scale combinations. To obtain scale variations in absolutely normalised distributions one has to simply nd the min/max in each bin. For the normalised distributions, one has to rst normalise each one of the seven curves within the desired range and then search for the min/max value in every bin. with the aim of having Monte Carlo error typically within 1% in each bin. pp ! ttj. For this reason we do not provide explicit results for the pT;tt distribution here. eV] 1.05 Ratio to mT/2 (all in NNLO QCD) eV] 1.05 Ratio to mT/2 (all in NNLO QCD) mt=173.3 GeV mt=173.3 GeV 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 400 600 800 1000 1200 1400 400 600 800 1000 1200 1400 pT,avt [GeV] pT,avt [GeV] eV] 1.05 Ratio to mT/2 (all in NNLO QCD) 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 400 600 800 1000 1200 1400 400 600 800 1000 1200 1400 eV] 1.05 Ratio to mT/2 (all in NNLO QCD) mt=173.3 GeV mt=173.3 GeV pT,avt [GeV] pT,avt [GeV] with NNLO pdf. Furthermore, the resummation of collinear logs this kinematic range. Above mtt 3:5 TeV the NNLO correction tends to be outside the NLO scale variation All with NNLO pdf All with NNLO pdf 1.2 Ratio to HT/4 (all in NNLO QCD) All with NNLO pdf All with NNLO pdf 1.2 Ratio to HT/4 (all in NNLO QCD) All with NNLO pdf All with NNLO pdf All with NNLO pdf All with NNLO pdf gure 6, but all partonic cross-sections (LO, NLO and NNLO) are computed with NNLO pdf. threshold and collinear resummation. The NNLO K-factor is rather mild for low although not as at as it is for a xed scale (see ref. [1]). The characteristic rise at absolute threshold noted in ref. [1] is also clearly visible. In Both are computed with NNPDF3.0 and with the optimal dynamic scale (3.9). We notice good within the scale error bands of the lower orders for both distributions. The MC errors the importance of the ytt distributions for ts of parton distribution functions in NNLO NLO LO mt=173.3 PP→ tt-+X (13 TeV) mt=173.3 GeV tt-+X (13 TeV) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 1.6-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 1.6-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 variation only. PP→ t-t+X (13 TeV) mt=173.3 GeV mt=173.3 GeV tt-+X (13 TeV) 1.2 0 250 500 750 100012501500175020002250250027503000 1.6 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 1.6 0 250 500 750 100012501500175020002250250027503000 1.8 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 scale variation only. from high-precision LHC data. as tables in the fastNLO library format [81, 82]. result computed in this work o ers the base for such future additions. Conclusions LHC collaborations over the span of LHC Run II. renormalisation and factorisation scale 0 . We derive such a scale based on the principle of Ratio to NNPDF30 (all in NNLO QCD) Ratio to NNPDF30 (all in NNLO QCD) 1.6-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 1.6-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2.5 -2 -1.5 -1 -0.5 from scale variation only. value of the NNLO+NNLL cross-section. The following scales satisfy our requirements best: 0 = mT =2 to be used for the description of the pT distribution of top/antitop quarks and 0 = HT =4 for all other di ers from the NNLO+NNLL tot(mt) value at the sub-percent level. scale candidates. For example, we nd that mtt-based dynamic scales are disfavoured, summed N3LO. pT;t=t and mtt. work. First, our approach to nding an appropriate dynamical scale is quite generic and has been used in the past in the context of NLO studies. Acknowledgments Open Access. This article is distributed under the terms of the Creative Commons any medium, provided the original author(s) and source are credited. Lett. 115 (2015) 052001 [arXiv:1411.3007] [INSPIRE]. fully-di erential top-quark pair production at the Tevatron, JHEP 05 (2016) 034 [arXiv:1601.05375] [INSPIRE]. [arXiv:1204.5201] [INSPIRE]. quark-gluon reaction, JHEP 01 (2013) 080 [arXiv:1210.6832] [INSPIRE]. [INSPIRE]. [INSPIRE]. 386] [hep-ph/0508091] [INSPIRE]. colliders, Eur. Phys. J. C 51 (2007) 37 [hep-ph/0610335] [INSPIRE]. pair production, Phys. Rev. D 74 (2006) 113005 [hep-ph/0610334] [INSPIRE]. (2008) 017503 [arXiv:0804.1237] [INSPIRE]. MCFM, PoS(DIS2015)130 [arXiv:1508.06247] [INSPIRE]. Phys. Rev. D 77 (2008) 014008 [arXiv:0708.1697] [INSPIRE]. [INSPIRE]. order, JHEP 02 (2011) 083 [arXiv:1012.4230] [INSPIRE]. [arXiv:1207.5018] [INSPIRE]. [arXiv:1305.7088] [INSPIRE]. [arXiv:1311.4893] [INSPIRE]. [INSPIRE]. [INSPIRE]. [INSPIRE]. LHC, JHEP 09 (2008) 127 [arXiv:0804.2800] [INSPIRE]. ibid. B 335 (1990) 260] [INSPIRE]. Phys. B 834 (2010) 116 [arXiv:1001.2312] [INSPIRE]. Phenomenology, Nucl. Phys. B 849 (2011) 296 [arXiv:1101.1300] [INSPIRE]. Colliders, JHEP 04 (2015) 145 [arXiv:1411.2588] [INSPIRE]. at NNLO, arXiv:1305.3892 [INSPIRE]. 097 [arXiv:1003.5827] [INSPIRE]. [INSPIRE]. [INSPIRE]. production, PoS(TOP2015)052 [arXiv:1512.02535] [INSPIRE]. [arXiv:1602.05612] [INSPIRE]. Phys. Rev. D 81 (2010) 074025 [arXiv:0910.3671] [INSPIRE]. [arXiv:0706.2569] [INSPIRE]. JHEP 11 (2001) 063 [hep-ph/0109231] [INSPIRE]. arXiv:0905.4739 [INSPIRE]. collisions at p collisions at p ibid. D 87 (2013) 119902] [arXiv:1212.6660] [INSPIRE]. 153 [Erratum JHEP 09 (2015) 141] [arXiv:1410.8857] [INSPIRE]. Tevatron Run-II, JHEP 10 (2014) 145 [arXiv:1407.7031] [INSPIRE]. [INSPIRE]. 70 [Erratum ibid. B 110 (1982) 501] [INSPIRE]. Charges, Phys. Rev. D 29 (1984) 2315 [INSPIRE]. (1989) 680 [INSPIRE]. D 26 (1982) 3656 [INSPIRE]. in Perturbative QCD, hep-ph/0703156 [INSPIRE]. Scheme Dependence, Nucl. Phys. B 277 (1986) 758 [INSPIRE]. Phys. Rev. D 67 (2003) 093005 [hep-ph/0301033] [INSPIRE]. Perturbative Quantum Chromodynamics, Phys. Rev. D 28 (1983) 228 [INSPIRE]. uncertainties, JHEP 09 (2011) 039 [arXiv:1105.5152] [INSPIRE]. (2015) 133 [arXiv:1409.5036] [INSPIRE]. 726 (2013) 266 [arXiv:1307.1843] [INSPIRE]. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE]. cross-section at the LHC, JHEP 05 (2016) 058 [arXiv:1602.00695] [INSPIRE]. in version 2 of the fastNLO project, arXiv:1208.3641 [INSPIRE]. [1] M. Czakon , D. Heymes and A. Mitov , High-precision di erential predictions for top-quark pairs at the LHC , Phys. Rev. Lett . 116 ( 2016 ) 082003 [arXiv:1511.00549] [INSPIRE]. [2] M. Czakon , P. Fiedler and A. Mitov , Resolving the Tevatron Top Quark Forward-Backward Asymmetry Puzzle: Fully Di erential Next-to-Next-to-Leading-Order Calculation , Phys. Rev. [3] M. Czakon , P. Fiedler , D. Heymes and A. Mitov , NNLO QCD predictions for [4] P. Barnreuther, M. Czakon and A. Mitov , Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to qq ! tt + X, Phys. Rev. Lett . 109 ( 2012 ) 132001 [5] M. Czakon and A. Mitov , NNLO corrections to top-pair production at hadron colliders : the [6] M. Czakon and A. Mitov , NNLO corrections to top pair production at hadron colliders : the [7] M. Czakon , P. Fiedler and A. Mitov , Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O( S4) , Phys. Rev. Lett . 110 ( 2013 ) 252004 [arXiv:1303.6254] [8] W. Beenakker , A. Denner , W. Hollik , R. Mertig , T. Sack and D. Wackeroth , Electroweak one [9] J.H. Kuhn , A. Scharf and P. Uwer , Electroweak corrections to top-quark pair production in [10] W. Bernreuther , M. Fucker and Z.-G. Si , Mixed QCD and weak corrections to top quark pair production at hadron colliders , Phys. Lett . B 633 ( 2006 ) 54 [Erratum ibid . B 644 ( 2007 ) [11] J.H. Kuhn , A. Scharf and P. Uwer , Electroweak e ects in top-quark pair production at hadron [12] W. Bernreuther , M. Fucker and Z.-G. Si , Weak interaction corrections to hadronic top quark [13] W. Bernreuther , M. Fucker and Z.-G. Si , Weak interaction corrections to hadronic top quark [15] J.H. Ku hn, A. Scharf and P. Uwer , Weak Interactions in Top-Quark Pair Production at [16] J.M. Campbell , D. Wackeroth and J. Zhou , Electroweak Corrections at the LHC with [17] W. Hollik and M. Kollar , NLO QED contributions to top-pair production at hadron collider , [19] D. Pagani , I. Tsinikos and M. Zaro , The impact of the photon PDF and electroweak corrections on tt distributions , Eur. Phys. J. C 76 ( 2016 ) 479 [arXiv:1606. 01915 ] [INSPIRE]. [20] A. Denner , S. Dittmaier , S. Kallweit and S. Pozzorini , NLO QCD corrections to WWbb production at hadron colliders , Phys. Rev. Lett . 106 ( 2011 ) 052001 [arXiv:1012.3975] [21] G. Bevilacqua , M. Czakon , A. van Hameren, C.G. Papadopoulos and M. Worek , Complete [22] A. Denner , S. Dittmaier , S. Kallweit and S. Pozzorini , NLO QCD corrections to o -shell [23] A.S. Papanastasiou , R. Frederix , S. Frixione , V. Hirschi and F. Maltoni , Single-top t-channel production with o -shell and non-resonant e ects , Phys. Lett . B 726 ( 2013 ) 223 [24] R. Frederix , Top Quark Induced Backgrounds to Higgs Production in the W W ( ) Decay Channel at Next-to-Leading-Order in QCD , Phys. Rev. Lett . 112 ( 2014 ) 082002 [25] F. Cascioli , S. Kallweit , P. Maierhofer and S. Pozzorini , A uni ed NLO description of top-pair and associated Wt production , Eur. Phys. J. C 74 ( 2014 ) 2783 [arXiv:1312.0546] [26] G. Bevilacqua , H.B. Hartanto , M. Kraus and M. Worek , Top Quark Pair Production in [27] R. Frederix , S. Frixione , A.S. Papanastasiou , S. Prestel and P. Torrielli , O -shell single-top [28] A. Mitov and G. Sterman , Final state interactions in single- and multi-particle inclusive [29] M. Cacciari , S. Frixione , M.L. Mangano , P. Nason and G. Ridol , Updated predictions for the [30] P. Nason , S. Dawson and R.K. Ellis , The One Particle Inclusive Di erential Cross-Section for Heavy Quark Production in Hadronic Collisions, Nucl . Phys . B 327 ( 1989 ) 49 [Erratum [31] W. Beenakker , W.L. van Neerven , R. Meng , G.A. Schuler and J. Smith, QCD corrections to [32] S. Forte , E. Laenen , P. Nason and J. Rojo , Heavy quarks in deep-inelastic scattering , Nucl. [33] R.D. Ball et al., Impact of Heavy Quark Masses on Parton Distributions and LHC [35] M. Czakon , P. Fiedler , A. Mitov and J. Rojo , Further exploration of top pair hadroproduction [36] M.L. Mangano , P. Nason and G. Ridol , Heavy quark correlations in hadron collisions at next-to-leading order, Nucl . Phys . B 373 ( 1992 ) 295 [INSPIRE]. [37] S. Frixione , M.L. Mangano , P. Nason and G. Ridol , Top quark distributions in hadronic collisions , Phys. Lett . B 351 ( 1995 ) 555 [hep-ph/9503213] [INSPIRE]. [38] V. Ahrens , A. Ferroglia , M. Neubert , B.D. Pecjak and L.L. Yang , Renormalization-Group [39] A. Ferroglia , B.D. Pecjak and L.L. Yang , Top-quark pair production at high invariant mass: an NNLO soft plus virtual approximation , JHEP 09 ( 2013 ) 032 [arXiv:1306.1537] [40] A. Ferroglia , B.D. Pecjak , D.J. Scott and L.L. Yang , QCD resummations for boosted top [41] B.D. Pecjak , D.J. Scott , X. Wang and L.L. Yang , Resummed di erential cross sections for top-quark pairs at the LHC , Phys. Rev. Lett . 116 ( 2016 ) 202001 [arXiv:1601.07020] [42] C.F. Berger et al., Precise Predictions for W + 4 - Jet Production at the Large Hadron Collider , Phys. Rev. Lett . 106 ( 2011 ) 092001 [arXiv:1009.2338] [INSPIRE]. [43] R. Boughezal , X. Liu and F. Petriello , A comparison of NNLO QCD predictions with 7 TeV ATLAS and CMS data for V + jet processes , Phys. Lett . B 760 ( 2016 ) 6 [44] K. Melnikov and G. Zanderighi , W + 3 jet production at the LHC as a signal or background , [45] J. Alwall et al., Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions , Eur. Phys. J. C 53 ( 2008 ) 473 [46] S. Catani , F. Krauss , R. Kuhn and B.R. Webber , QCD matrix elements + parton showers , [47] C.W. Bauer and B.O. Lange , Scale setting and resummation of logarithms in pp ! V + jets , [51] ATLAS collaboration, Measurement of dijet cross sections in pp collisions at 7 TeV [52] P. Francavilla , Measurements of inclusive jet and dijet cross sections at the Large Hadron Collider, Int . J. Mod . Phys . A 30 ( 2015 ) 1546003 [arXiv:1510. 01943 ] [INSPIRE]. [53] G. Grunberg , Renormalization Group Improved Perturbative QCD, Phys. Lett. B 95 ( 1980 ) [54] G. Grunberg , Renormalization Scheme Independent QCD and QED: The Method of E ective [55] G. Grunberg , On Some Ambiguities in the Method of E ective Charges, Phys. Rev. D 40 [56] P.M. Stevenson , Optimized Perturbation Theory, Phys. Rev. D 23 ( 1981 ) 2916 [INSPIRE]. [57] J. Kubo and S. Sakakibara , Equivalence of the Fastest Apparent Convergence Criterion and [59] C.J. Maxwell and A. Mirjalili , Complete renormalization group improvement: Avoiding [62] F. Maltoni , Z. Sullivan and S. Willenbrock , Higgs-boson production via bottom-quark fusion , [63] S.J. Brodsky , G.P. Lepage and P.B. Mackenzie , On the Elimination of Scale Ambiguities in [64] S.J. Brodsky and L. Di Giustino , Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality , Phys. Rev . D 86 ( 2012 ) 085026 [arXiv:1107.0338] [INSPIRE]. [65] S.J. Brodsky and X.-G. Wu , Scale Setting Using the Extended Renormalization Group and [66] S.J. Brodsky and X.-G. Wu , Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality , Phys. Rev. Lett . 109 ( 2012 ) [69] H.-H. Ma , X.-G. Wu , Y. Ma , S.J. Brodsky and M. Mojaza , Setting the renormalization scale sequential extended Brodsky-Lepage-Mackenzie approach , Phys. Rev . D 91 ( 2015 ) 094028 [70] M. Cacciari and N. Houdeau , Meaningful characterisation of perturbative theoretical [71] E. Bagnaschi , M. Cacciari , A. Gu anti and L. Jenniches, An extensive survey of the [72] A. David and G. Passarino , How well can we guess theoretical uncertainties? , Phys. Lett . B [73] A. Buckley et al., LHAPDF6: parton density access in the LHC precision era , Eur. Phys. J. [74] A.D. Martin , W.J. Stirling , R.S. Thorne and G. Watt , Parton distributions for the LHC , Eur. Phys. J. C 63 ( 2009 ) 189 [arXiv:0901.0002] [INSPIRE]. [75] NNPDF collaboration , R.D. Ball et al., Parton distributions for the LHC Run II , JHEP 04 [76] M. Czakon and A. Mitov , Top++: A Program for the Calculation of the Top-Pair Cross-Section at Hadron Colliders , Comput. Phys. Commun . 185 ( 2014 ) 2930 [77] C. Anastasiou et al., High precision determination of the gluon fusion Higgs boson [78] S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics , Phys. Rev. D 93 ( 2016 ) 033006 [arXiv:1506.07443] [INSPIRE]. [79] L.A. Harland-Lang , A.D. Martin , P. Motylinski and R.S. Thorne , Parton distributions in the LHC era: MMHT 2014 PDFs, Eur . Phys. J. C 75 ( 2015 ) 204 [arXiv:1412.3989] [INSPIRE]. [80] V. Bertone , S. Carrazza and J. Rojo , APFEL: A PDF Evolution Library with QED corrections, Comput . Phys. Commun . 185 ( 2014 ) 1647 [arXiv:1310.1394] [INSPIRE]. [81] T. Kluge , K. Rabbertz and M. Wobisch , FastNLO: Fast pQCD calculations for PDF ts, [82] fastNLO collaboration , D. Britzger , K. Rabbertz , F. Stober and M. Wobisch , New features [83] U. Langenfeld , S.-O. Moch and P. Uwer , Measuring the running top-quark mass , Phys. Rev. [84] M. Dowling and S.-O. Moch , Di erential distributions for top-quark hadro-production with a running mass , Eur. Phys. J. C 74 ( 2014 ) 3167 [arXiv:1305.6422] [INSPIRE].


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP04%282017%29071.pdf

Dynamical scales for multi-TeV top-pair production at the LHC, Journal of High Energy Physics, 2017, DOI: 10.1007/JHEP04(2017)071