We discuss a global fit of top quark BSM couplings, phrased in the
model-independent language of higher-dimensional effective operators, to the
currently available data from the LHC and Tevatron. We examine the interplay
between inclusive and differential measurements, and the complementarity of LHC
and Tevatron results. We conclude with a discussion of projections for
improvement over LHC Run II.Comment: 5 pages, 4 figures, proceedings of the 9th International Workshop on
  the CKM Unitarity Triangle, 28 November - 3 December 2016, Tata Institute for
  Fundamental Research (TIFR), Mumbai, Indi

Buckley, Andy

Englert, Christoph

Ferrando, James

Miller, David J.

Moore, Liam

Nordström, Karl

Russell, Michael

White, Chris D.

English

arXiv

We discuss a global fit of top quark BSM couplings, phrased in the model-independent language of higher-dimensional effective operators, to the currently available data from the LHC and Tevatron. We examine the interplay between inclusive and differential measurements, and the complementarity of LHC and Tevatron results. We conclude with a discussion of projections for improvement over LHC Run II

DESY

Results from TopFitter

Nordstrom, Karl

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PoS(CKM2016)127Results from TopFitterAndy BuckleySUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdomE-mail: andy.buckley@glasgow.ac.ukChristoph EnglertSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdomE-mail: christoph.englert@glasgow.ac.ukJames FerrandoDESY, D-22607 Hamburg, GermanyE-mail: james.ferrando@desy.deDavid J. MillerSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdomE-mail: david.j.miller@glasgow.ac.ukLiam MooreCentre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique deLouvain, B-1348 Louvain-la-Neuve, BelgiumE-mail: l.moore@cern.chKarl NördstromSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdomE-mail: k.nordstrom.1@research.gla.ac.ukMichael Russell∗SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UnitedKingdomE-mail: m.russell.2@research.gla.ac.ukChris D. WhiteCentre for Research in String Theory, School of Physics and Astronomy, Queen Mary Universityof London, 327 Mile End Road, London E1 4NS, UKE-mail: christopher.white@qmul.ac.ukWe discuss a global fit of top quark BSM couplings, phrased in the model-independent languageof higher-dimensional effective operators, to the currently available data from the LHC and Teva-tron. We examine the interplay between inclusive and differential measurements, and the com-plementarity of LHC and Tevatron results. We conclude with a discussion of projections forimprovement over LHC Run II.9th International Workshop on the CKM Unitarity Triangle28 November - 3 December 2016Tata Institute for Fundamental Research (TIFR), Mumbai, Indiac© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/PoS(CKM2016)127Results from TopFitter Michael Russell1. IntroductionThe lack of convincing signals of new physics in the data from the Tevatron and LHC has ledto the resurgence of model-independent frameworks for parameterising deviations from StandardModel predictions. It also suggests that if there is new physics, there is either a large separation inenergy between the scale that it resides at; Λ, and the scales probed by the LHC; E, or that it is veryweakly coupled, or both. In either case, the Standard Model can be viewed as the leading set termsin an effective field theory (EFT), where the non-SM interactions are captured by an infinite seriesof higher-dimensional (that is, D > 4) operators, which, by virtue of their renormalisation groupscaling, become increasingly important at higher energy scales. The leading effects on colliderobservables enter at dimension D = 6, and the series is typically truncated at the same order, whichis justified provided that E Λ. The Standard Model EFT can then be succinctly summarised asLfull = LSM +∑iciOiΛ2. (1.1)The sum in Eq. (1.1) runs over a total of 59 operators Oi. In the absence of a specific high-energy model to match to, the dimensionless Wilson coefficients ci are all free parameters that mustbe extracted from data. Clearly, performing a simultaneous fit of 59 free parameters is unfeasible.When one considers a specific class of observables, however, the relevant operator set is muchsmaller than this. The EFT fit procedure is then straightforward: Firstly, one gathers a set ofobservables that may be thought of as sensitive to potential new physics effects. Secondly, onewrites down all the operators that can affect these observables. Finally, one computes the effectsof these operators on the observables and fits to the data, thus extracting values or bounds on theircorresponding Wilson coefficients.The top quark sector is a well-motivated place to look for the effects of dimension-6 oper-ators. The top quark plays a special role in most scenarios that explain electroweak symmetrybreaking, scenarios which in turn typically predict modified top couplings which can be modelledby dimension-6 operators, provided the assumptions stated in the first paragraph are satisfied. Inaddition, the plethora of top quark measurements available from the LHC and Tevatron allows topcouplings to be scrutinised with high precision in a global fit. This talk summarises the results ofsuch a fit.2. Global fit to Tevatron and LHC Run I dataWith the assumptions of C P-conservation and minimal flavour violation, the complete1 setof operators from Eq. (1.1) that modify the couplings of the top quark areO(1)qq = (q̄γµq)(q̄γµq) OuW = (q̄σ µντ Iu)ϕ̃W Iµν O(3)ϕq = i(ϕ†←→D Iµϕ)(q̄γµτIq)O(3)qq = (q̄γµτ Iq)(q̄γµτ Iq) OuG = (q̄σ µνT Au)ϕ̃GAµν O(1)ϕq = i(ϕ†←→D µϕ)(q̄γµq)∗Speaker.1In this analysis, we work at leading order in the EFT; that is, we do not consider operators induced by mixing orloops.1PoS(CKM2016)127Results from TopFitter Michael RussellOuu = (ūγµu)(ūγµu) OG = fABCGAνµ GBλν GCµλOuB = (q̄σ µνu)ϕ̃BµνO(8)qu = (q̄γµT Aq)(ūγµT Au) OG̃ = fABCG̃Aνµ GBλν GCµλOϕu = (ϕ†i←→D µϕ)(ūγµu)O(8)qd = (q̄γµTAq)(d̄γµT Ad) OϕG = (ϕ†ϕ)GAµνGAµν OϕG̃ = (ϕ†ϕ)G̃AµνGAµνO(8)ud = (ūγµTAu)(d̄γµT Ad) . (2.1)For a complete discussion of the notation used, and the phenomenology of each operator, thereader is referred to Refs [1, 2]. This operator set of Eq. (2.1) was implemented in FeynRules[3],and interfaced via UFO[4] to MadGraph[5], which was used to generate theory predictions ateach sample point in the parameter space of Wilson coefficients. Higher-order QCD correctionsto these observables were taken into account with MCFM[6] and MC@NLO[5], with associatedscale and PDF uncertainties. Using techniques from Ref. [7], a polynomial function was used tointerpolate between each sample point, thus building up a smooth picture of the dependence ofeach observable used on each operator. A test statistic was constructed; in our case a correlated χ2,between theory and data, and used to draw exclusion contours on the Wilson coefficients Ci. Theinput measurements used in the fit are summarised in Fig. 1.Figure 1: The measurements entering our fit. See Ref. [2] for more details.The main result of our fit is that all operator coefficients are consistent with zero at the 95%confidence interval. It is interesting to ask which observables have the dominant pull on the fit. Weaddress this question in Fig. 2, where we show the joint 68%, 95% and 99% confidence intervals on2PoS(CKM2016)127Results from TopFitter Michael Russell−0.2 −0.1 0.0 0.1 0.2C̄G−0.4−0.3−0.2−0.10.00.10.2C̄1 u−0.2 −0.1 0.0 0.1 0.2C̄33uG−0.2−0.10.00.1C̄1 uFigure 2: 2-dimensional 68%, 95% and 99% confidence intervals on pairs of operators contribut-ing to top pair production. Left: lines represent constraints obtained using total cross-sectionsonly; contours are obtained using differential measurements as well. Right: lines are obtainedusing Tevatron data; contours are obtained using only LHC Run I data.a pair of operators that modify top pair production. On the left, the lines are the bounds obtainedusing inclusive cross-section measurements only, whereas the filled contours include differentialdistributions as well. This shows that differential measurements are the most sensitive observablein constraining D = 6 operators. On the right, the lines are the bounds obtained using Tevatron tt̄measurements only, whereas the contours are obtained using only LHC Run I data, showing thatthe LHC has already overtaken the Tevatron in terms of sensitivity, owing to the larger statisticalsample collected there.In addition to top pair production, we also examine single top production, associated pairproduction with a Z or a γ , various charge asymmetries in tt̄ production, as well as observablesrelating to the top quark decay; namely helicity fractions and indirect measurements of the topwidth. The final 95% confidence intervals on the operators we consider are presented in Fig. 3.The constraints are presented in two ways: firstly, we fit to each operator one at a time (red), orin a global fit where we marginalise over all the remaining operators (blue). No finite marginalconstraint is obtained on the final three operators, due to their much weaker impact on the fit thanthe rest of the operator set. Again, we refer the reader to Ref. [2] for a more detailed discussion ofall of these points.3. Improving the fit with boosted observablesThe Wilson coefficient bounds presented in Fig. 3 are rather weak, and approach the regionwhere the D = 6 EFT description may no longer be valid. If we take Ci = 1, for instance, we typi-cally find bounds of Λ & 500 GeV. This scale is resolved by several of the measurements enteringour fit; namely the high-energy tails of the kinematic distributions, thus violating the conditionEΛ that motivated the EFT in the first place. To try to isolate the regions of phase-space that aremost sensitive to D = 6 operators, we perform an analysis of boosted (ptT > 200 GeV) top pair pro-3PoS(CKM2016)127Results from TopFitter Michael Russell-1 -0.5 0 0.5 1C̄i = Civ2/Λ2individualmarginalizedC̄GC̄33uGC̄1uC̄2uC̄1dC̄2dC̄33uWC̄tC̄3φqC̄33uBC̄φuC̄1φqFigure 3: Individual (red) and marginal (blue) 95% confidence limits on the Wilson coefficientsfor each operator we consider in this fit. Figure taken from Ref. [2].duction in the semileptonic decay channel, by merging the decay products of the hadronic top intoa fat jet, and reconstructing the top pT using HepTopTagger[8]. For ptT < 200 GeV we perform astandard resolved analysis. We fit the operators of Eq. (2.1) that contribute to tt̄ production to Stan-dard Model pseudodata in both the resolved and boosted regions. Theory uncertainties are treatedas before. On the experimental side, we take statistical uncertainties corresponding to 30 fb−1 ofSM data, and assume a 20% statistical uncertainty on each bin. We then ask: what improvementscan be made on current bounds when systematic and statistical uncertainties are reduced?The results of this analysis are shown in Fig. 4. The conclusions are quite different for theresolved and the boosted selections. For the former, improvements can be made both by takingmore data and by reducing systematics, but reducing systematics is more important. Taking C1uas an example, we see that improving systematics by 10% and taking 300 fb−1 of data producesa comparable bound to keeping current systematics and taking a tenfold larger data sample. Forthe boosted case, on the other hand, we see that, at low statistics there is no gain from reducingsystematics, which merely reflects that high-pT boosted measurements are statistics limited at thisstage. Even with larger data samples, the gain to be made by reducing systematics is more modest.This says that another input to the fit becomes important: the theoretical modelling of the high-pTtail. Approaching 3000 fb−1, theory uncertainties will become the main driving force in improvingthe top EFT fit at the LHC. Therefore, there is work to be done on both sides if the LHC is to reachits full potential for measuring or placing limits on D = 6 operators.AcknowledgementsThe speaker wishes to thank the organisers of the CKM workshop, especially the convenorsof the top working group; Veronique Boisvert and Joachim Brod, for the pleasant and productive4PoS(CKM2016)127Results from TopFitter Michael Russell00.20.40.60.81CG C33uG C1u C2u C1d C2d∆Ci/∆Ci@20%syst,30fb−1Resolved selection00.20.40.60.81CG C33uG C1u C2u C1d C2dBoosted selectionFigure 4: Fractional improvement on the 95% confidence intervals for the tt̄ operators. The greenbar represents the 95% confidence limit obtained from 20% systematic uncertainty and 30 fb−1 ofdata. The purple and blue bars represent the fractional improvement with respectively, 300 fb−1and 3 ab−1 of data, also at 20% systematics, while the yellow, orange and red are the analogousdata sample sizes for 10% systematics. Figure taken from Ref. [9].atmosphere throughout.References[1] A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Russell, and C. D. White, Global fit oftop quark effective theory to data, Phys. Rev. D92 (2015), no. 9 091501, [arXiv:1506.0884].[2] A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Russell, and C. D. White, Constrainingtop quark effective theory in the LHC Run II era, JHEP 04 (2016) 015, [arXiv:1512.0336].[3] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, FeynRules 2.0 - A complete toolboxfor tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250–2300,[arXiv:1310.1921].[4] C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer, et. al., UFO - The Universal FeynRulesOutput, Comput.Phys.Commun. 183 (2012) 1201–1214, [arXiv:1108.2040].[5] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, et. al., The automated computation oftree-level and next-to-leading order differential cross sections, and their matching to parton showersimulations, JHEP 1407 (2014) 079, [arXiv:1405.0301].[6] J. M. Campbell and R. K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. Proc. Suppl.205-206 (2010) 10–15, [arXiv:1007.3492].[7] A. Buckley, H. Hoeth, H. Lacker, H. Schulz, and J. E. von Seggern, Systematic event generator tuningfor the LHC, Eur. Phys. J. C65 (2010) 331–357, [arXiv:0907.2973].[8] G. Kasieczka, T. Plehn, T. Schell, T. Strebler, and G. P. Salam, Resonance Searches with an UpdatedTop Tagger, JHEP 06 (2015) 203, [arXiv:1503.0592].[9] C. Englert, K. Nordstrom, L. Moore, and M. Russell, Giving top quark effective operators a boost,Phys. Lett. B763 (2016) 9–15, [arXiv:1607.0430].5

Michael Russell

Andy Buckley

Christoph ENGLERT

James Ferrando

Liam MOORE

Karl Nördstrom

David Miller

Chris White

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