Cavendish-HEP-14/15TTK-15-02

Summary of the Topical Workshop on Top Quark

Differential Distributions 2014

Michal Czakon

Institut fur Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, D-52056Aachen, Germany

E-mail: mczakon@physik.rwth-aachen.de

Alexander Mitov

Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK

E-mail: adm74@cam.ac.uk

Juan Rojo

Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, University of Oxford, OX1 3NPOxford, UK

E-mail: juan.rojo@physics.ox.ac.uk

Abstract. We summarise the Topical Workshop on Top Quark Differential Distributions2014, which took place in Cannes immediately before the annual Top2014 conference. Theworkshop was motivated by the availability of top quark differential distributions at NNLOand the forthcoming LHC 13 TeV data. The main goal of the workshop was to explore theimpact of improved calculations of top quark production on precision LHC measurements, PDFdeterminations and searches for physics beyond the Standard Model, as well as finding waysin which the high precision data from ATLAS, CMS and LHCb can be used to further refinetheoretical predictions for top production.

1. IntroductionThe forthcoming availability of fully differential results for top quark production at NNLO,together with the upcoming restart of the LHC at 13 TeV, prompted us to organise a workshopcentred around theoretical aspects of precision top physics. The workshop was held 26–28September 2014 in Cannes, i.e. it immediately preceded the annual Top2014 conference.

The workshop brought together a group of theory experts working on top quark physics andclosely related subjects such as parton distribution functions, parton showers and soft gluonresummation. The presence of experts in BSM physics involving top quarks was essential, aswas the participation of top quark experts from ATLAS, CMS and LHCb.

The main goal of the workshop was to explore the phenomenological implications of theongoing progress in precision calculations for top quark production, both in terms of fullydifferential NNLO results and in terms of realistic description of final states provided by NLOcalculations matched to parton showers.

The main questions that were discussed included: which top quark differential distributionsare theoretically and experimentally more interesting; what is the impact of present and futuretop quark data on PDF fits; progress in realistic final states with decaying top quarks; finitetop quark width corrections and matching to parton showers; the role of soft and collinear

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Figure 1. Schematic illustration of recent theoretical progress in theory calculations of top quarkproduction in complementary directions: NNLO calculations, merging of NLO+PS samples of differentmultiplicities and results beyond stable tops (courtesy of M. Schultze).

In the following, we present a concise summary of the discussions that took place during theworkshop. The complete agenda, with presentation slides, is available at the workshop webpage:

http://indico.cern.ch/e/top-differential-distributions-2014

Given the space limitation, we are unfortunately unable to cover in full detail everything thatwas discussed at the workshop.

2. Top quark production and NNLO calculationsRecent progress in techniques for NNLO QCD calculations [1–8] has led in the last few years toa dramatic increase in the availability of NNLO calculations for hadron collider processes withcomplex final states. The NNLO result for the total top quark pair production cross-section hasbeen available for a while [9–12]. During the workshop, preliminary results on the extension ofthis calculation to differential distributions were presented. These NNLO results are consistentwith the NLO scale variation estimate, and their inclusion leads to a significant reduction of thetheory uncertainties. This is illustrated in Fig. 2, where we show the invariant mass distributionMtt for top quark pair production at the Tevatron at NNLO. These results have also recentlybeen used to compute the corrections to the forward-backward asymmetry at the Tevatron inNNLO QCD [13], showing that perturbative corrections increase the absolute Standard Model(SM) value of the asymmetry by about 2%, thus improving the agreement of SM prediction withthe measurements from CDF and DØ Collaborations.

Related techniques have also lead to the recent computation of the NNLO corrections tosingle top production [14], which was also discussed at the workshop. As an illustrative result,

Top pair at NNLO Alexander Mitov Cannes, 26 Sep 2014

Czakon, Fiedler, Mitov, preliminary

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tion (DFG) via the Sonderforschungsbereich/TransregioSFB/TR-9 “Computational Particle Physics”, and theHeisenberg programme. The work of A. M. is supportedby the UK Science and Technology Facilities Council[grants ST/L002760/1 and ST/K004883/1].

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Errors due to scale variation only

Single-top @ NNLO: more differential observables

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TABLE I: QCD corrections to t-channel single top quark production cross sections at 8 TeV LHC with a cut on the transversemomentum of the top quark p⊥. Cross sections are shown at leading, next-to-leading and next-to-next-to-leading order independence of the factorization and renormalization scale µ = mt (central value), µ = 2mt (upper value) and µ = mt/2 (lowervalue). Corrections at NLO and at NNLO (relative to the NLO) are shown in percent for µ = mt.

las for the phase-space parametrization relevant for theub → dt, ub → dtg and ub → dtgg sub-processes, as wellas a discussion of an appropriate choices of variables rel-evant for the extraction of singularities can be found inthat reference. Using the language of that paper, we onlyneed to consider “initial-state” sectors since there are nocollinear singularities associated with final state particlesdue to the fact that top quarks are massive. All calcula-tions required for initial-state sectors are documented inRef. [61] except that here we need soft and collinear lim-its for incoming quarks, rather than gluons, and the softcurrent for a massive particle. This, however, is a minordifference that does not affect the principal features ofthe computational method.

The above discussion of the NNLO QCD correctionsto the heavy quark line can be applied almost verba-tim to corrections to the light quark line. The two-loopcorrections for the 0 → qq′W ∗ vertex are known sincelong ago [62–64]. One-loop corrections to 0 → qq′gW ∗

scattering are also well-known; we implemented the re-sult presented in [65] and again checked the implemen-tation against an independent computation based on thePassarino-Veltman reduction. Apart from different am-plitudes, the only minor difference with respect to cor-rections to the heavy quark line is that in this case thereare collinear singularities associated with both, the in-coming and the outgoing quark lines. We deal with thisproblem splitting the real-emission contribution into sec-tors, see Ref. [61]. In the language of that paper, wehave to consider “initial-initial”, “final-final” and mixed“initial-final” sectors. Finally, we briefly comment on thecontribution shown in Fig.1c. We note that, althoughformally NNLO, it is effectively the product of NLO cor-rections to the heavy and the light quark lines, so thatit can be dealt with using techniques familiar from NLOcomputations.

We will now comment on our treatment of γ5. Forperturbative calculations at higher orders the presence ofthe Dirac matrix γ5 is a nuisance since it can not be con-tinued to d-dimensions in a straightforward way. Whilecomputationally-efficient ways to deal with γ5 in com-putations, that employ dimensional regularization, exist(see e.g. Ref. [66]), they are typically complex and un-transparent. Fortunately, there is a simple way to solvethe γ5 problem in our case. Indeed, in the calculation ofvirtual corrections to the tWb weak vertex, γ5 is taken

to be anti-commuting [40–43]. This enforces the left-handed polarization of the b-quark and removes the issueof γ5 altogether. Indeed, if we imagine that the weakb → t transition is facilitated by the vector current butwe select the b-quark with left-handed polarization only,we will obtain the same result as when the calculation isperformed with the anti-commuting γ5. Since the can-cellation of infra-red and collinear divergences occurs foreach polarization of the incoming b-quark separately, thisapproach completely eliminates the need to specify thescheme for dealing with γ5 and automatically enforcessimultaneous conservation of vector and axial currents –a must-have feature if quantum anomalies are neglected.Of course, this requires that we deal with the γ5 appear-ing in real emission diagrams in the same way as in thevirtual correction and this is, indeed, what we do by us-ing helicity amplitudes, as described in [39].

We have performed several checks to ensure that ourcalculation of NNLO QCD corrections to single top quarkproduction is correct. For example, we have compared allthe tree-level matrix elements that are used in this com-putation, e.g. ub → dt+ng, with 0 ≤ n ≤ 2, ub → dt+qq,ug → dbt + mg, 0 ≤ m ≤ 1, against MadGraph [67] andfound complete agreement. We have extracted one-loopamplitudes for 0 → Wtbg from MCFM [45] and checkedthem against our own implementation of the Passarino-Veltman reduction, for both the W ∗b → tg and theW ∗g → tb processes. We have cross-checked one-loopamplitudes for W ∗u → dg and related channels againstMadLoop [68]. In the intermediate stages of the compu-tation, we also require reduced tree and one-loop ampli-tudes computed to higher orders in ϵ, as explained e.g. inRef. [61]. We checked that their contributions drop outfrom the final results, in accord with the general conclu-sion of Ref. [69].

One of the most important checks is provided by thecancellation of infra-red and collinear divergences. In-deed, the technique for NNLO QCD computations de-scribed in Refs. [47–49] leads to a Laurent expansionof different contributions to differential cross sections inthe dimensional regularization parameter ϵ; coefficientsof this expansion are computed by numerical integra-tion. Independence of physical cross sections on the reg-ularization parameter is therefore achieved numerically,when different contributions to such cross sections (two-loop virtual corrections, one-loop corrections to single

•Contrary to NLO, results stable in the full spectrum!

•Scale dependence typically improved!

•K-factor is small but not constant

Figure 2. Left plot: preliminary results for the invariant mass distribution Mtt for top quark pairproduction at the Tevatron at NNLO accuracy. Right plot: NNLO cross-section for the production ofsingle top quarks at the LHC 7 TeV, as a function of the cut in the pT of the top quark [14].

in Fig. 2 we show the cross-section as a function of the cut in the pT of the top quark, for theLHC 7 TeV. For this observable the NNLO corrections also lead to a substantial improvementin the perturbative expansion. Another central process of the LHC program is dijet production,due to its relevance for precision Standard Model measurements, PDF determinations and newphysics searches. Recent results towards the full NNLO calculation [15] were presented in theworkshop. Several other important LHC processes have also become available at NNLO, see forinstance [16–18]. More processes/observables will be computed in the near future, underscoringthe trend towards NNLO QCD becoming the standard for precision phenomenology at the LHC.However, work is still required to be able to use these calculations with realistic final states, aswe report below.

3. Top pair production with realistic final statesThe current state-of-the-art simulations of top quark production and decay utilize mergedNLO calculations matched to parton showers. Various proposals for NLO merging have beenintroduced recently, including the FxFx merging [19], the UNLOPS procedure [20] and theMEPS@NLO [21] method among others. The implications of some of these updated calculationsfor top quark pair production were discussed at the workshop. As a representative result, inFig. 3 we show the HT distribution in tt+jets events at LHC 7 TeV within the MEPS@NLOapproach, compared to predictions based on samples with exclusive jet multiplicities. Clearly,the individual multiplicities contribute differently depending on the value of HT , while the NLOmerged sample could be applied to the full phase space. There has also been important progressin the matching of NNLO calculations to parton showers [22,23], though still quite some work isneeded to be able to apply these methods to top quark production. Some preliminary results formatching to the Nagy-Soper parton shower with quantum interference [24] at NLO have beenpresented [25]. Though they are still restricted to on-shell top-quarks, work in the direction ofrealistic final states is under way.

Another important application of the recent progress in top physics calculations is toprecision top quark mass determination. For instance, the top quark mass mt can be extractedfrom template fits to the mlb invariant mass distribution with good experimental precision.However, unless the NLO corrections to the pp→WbWb process are accounted for, theoreticaluncertainties due to missing higher orders will dominate the total mt uncertainty. In Fig. 3we show the mlb distribution computed at NLO at the LHC 7 TeV, for different values of the

NLO merging in tt+jets – examples of observables[HOCHE, KRAUSS, MAIERHOFER, POZZORINI, SCHONHERR, SIEGERT, ARXIV:1402.6293]

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Figure 3. Left plot: HT distribution in tt+jets events at the LHC 7 TeV in the MEPS@NLO approach,compared to samples with exclusive jet multiplicities. Right plot: the mlb distribution computed at NLOat the LHC 7 TeV, for different values of the top quark mass.

top quark mass [26]. Similar conclusions, of course, also applies to many other differentialdistributions whose accurate prediction is an important ingredient in new physics searches.

4. Experimental issuesOne of the workshop’s main objectives was to initiate a discussion about how ongoing theoreticalprogress and current and future experimental measurements can improve each other. Some of thediscussed issues were triggers, pile-up subtraction, theory uncertainties that affect the selectionefficiency, improvements in Monte Carlo simulations, definitions of physical observables and topquark reconstruction.

In this context, one of the most important topics for discussion was how the availability ofNNLO top quark differential distributions, as well as improvements in the description of realisticfinal states at NLO, can help in reducing various extrapolation errors. Since state-of-the-artMC simulations are now based on NLO calculations that are merged for different topologies andmatched to parton showers, it will be essential for precision top physics at LHC Run II to adoptthese tools as standard. The availability of differential predictions, either NNLO with stable topsor NLO+PS with realistic final states, represents a strong motivation for all LHC measurementsto be provided directly in the fiducial region, and that comparisons with theory are performedat this level. Such a “meeting point” between theory and experiment avoids inconsistencies invarious comparisons or, equivalently, the unnecessary increase of theoretical uncertainties in theextrapolation to the full phase space. Of course inclusive measurements are also important inmany cases, for example in comparisons with other experiments, but the original informationin the fiducial region should also be available. In this respect, an important improvement inrealistic analyses would be the extension of the NNLO calculation to the case of unstable tops.

An important ingredient in top production predictions made with MC event generators isthe tune for the semi-hard and soft physics. Such tunes are typically performed with LO MonteCarlos (see for example the recent Monash 2013 Tune [27] of Pythia8 [28]) and then appliedto NLO+PS generators. Given the importance of non-perturbative and semi-hard physics invarious top quark measurements, it would be of utmost importance to produce dedicated newtunes for NLO generators that are able to describe simultaneously the hard, semi-hard and softdynamics. Work along these lines is ongoing within the ATLAS and CMS collaborations, withthe aim of obtaining dedicated NLO tunes that can then be applied to top physics at Run II.

Also discussed at the workshop was the possibility to present top measurements in terms ofratios of various cross-sections, in order to partially cancel some of the leading experimental andtheoretical uncertainties. For instance, in early Run II data the LHC luminosity uncertaintycould be substantial, and measurements of ratios like σ(tt)/σ(Z) should allow to performprecision top quark physics already from the first months of data taking. Related proposalsinclude ratios such as σ(ttbb)/σ(ttjj), which also provide stringent tests of MC event generators.

In addition, the ratios of top quark cross-sections between 13 TeV and 8 TeV provide a uniqueopportunity to constrain the gluon PDF with greatly reduced theory uncertainties from scaleand mt. The advantages of presenting the measurements of top quark differential distributionseither with absolute normalization or normalized to the fiducial cross-section were also discussed.The consensus in the community is that the measurements should be presented both ways, i.e.if normalized measurements are published, the normalization factor should be provided as well.We recall that while for many analyses (for example searches) only an accurate measurementof the shape of the distribution is required, for others (in particular PDF analyses) the overallnormalization provides precious additional information.

An important topic of the discussion was how to optimize the use of theoretical calculationswhen kinematical distributions are used to extract SM parameters such as αS(MZ) and mt.For instance, CMS has extracted αS(MZ) from the inclusive tt cross-sections using the inclusiveNNLO calculation [29] and it would be interesting to repeat the extraction from differentialdistributions. Concerning mt extractions, it became clear that it is essential to quantify thetheory uncertainties from template fits of kinematical distributions; in particular NLO QCDshould be the baseline for the computation of these templates (since LO calculations have largeassociated scale uncertainties). The use of double differential measurements could be beneficialhere, provided one is not limited by statistics.

Finally, we discussed the fact that many searches that utilise measurements with top quarksin the final state are never unfolded and recast in terms of differential SM measurements.Translating searches into SM measurements could be very beneficial since, first, these allownew precision SM studies in extreme kinematical regions, and second, existing searches couldeasily be re-applied to different BSM scenarios.

5. Top quark data and PDF fitsAt the LHC, top quark pairs are produced predominantly in the gluon-gluon initial state.Therefore, the recent improvements in the precision of both experimental measurements andtheoretical calculations for top pair production strongly suggest that top data should provideuseful constraints on the poorly-known large-x gluon PDF, fully complementary to thoseobtained from other processes like jet production [30] or photon production [31, 32]. Severalstudies have demonstrated that already at the level of inclusive cross-sections, available topquark data from ATLAS and CMS at 7 TeV and 8 TeV can provide important information onthe gluon for x ∼> 0.1 [33–35]. In addition, the feasibility of top quark production in the forwardregion by LHCb and the possible constraints in PDFs that such data would provide has alsobeen quantified [36]. Total cross-sections for tt production are already included in the recentNNPDF3.0 [37] and MMHT14 [38] global analysis, and are also available in the HERAfitter

open-source QCD fit framework [39].The challenge now is to include the differential distributions of top pairs into global PDF

analysis, using both the NNLO results and the recent availability of experimental measurementsfrom ATLAS and CMS [41–43]. In Fig. 4 we show the recent ATLAS 7 TeV differentialmeasurements [42] compared with different PDF sets: including these data into PDF fit willprovide a handle on the large-x gluon. In exploiting these measurements, it will be necessaryto exploit the full power of recent theory calculation for these distributions, by combining fastinterfaces to NLO calculations like aMCfast [44], where the APPLgrid [45] framework is used

2

Here are the normalised distributions compared to various NLO PDFs.HERAPDF with its softer high-x gluon is doing quite wellEW corrections are not applied.

The data are the combined electron and muon data supplied in Table V of the paper

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the default fit and after including the Tevatron and LHC top quark cross section data. Right plot:

the relative reduction of PDF uncertainties thanks to the inclusion of top data in the PDF fit.

negligible.

It is interesting to study the modifications of the theory predictions after the top

quark data have been added into the NNPDF2.3 fit. In Table 9 we show the tt cross

section for NNPDF2.3, comparing the default prediction with the predictions after adding

different subsets of the top quark data. We show only the entries which correspond to pure

predictions. By including top data from lower energy colliders, we can provide arguably

the most accurate theoretical prediction for the total tt cross section at higher energies,

given that PDF uncertainties will be reduced in the same kinematical range from lower

energy data.11

These predictions are collected in Table 9. As an illustration, the NNPDF2.3 prediction

including Tevatron and LHC 7 top data would be the best available theory prediction for

LHC 8 TeV. Note that not only PDF uncertainties are reduced, but that also the central

value is shifted to improve the agreement with the experimental data. As can be seen, the

precise 7 TeV data carry most of the constraining power, though of course improved power

of the 8 TeV data will be provided with the analysis of the full 2012 dataset.

Then in Table 10 we provide NNPDF2.3 χ2 compared to the top quark data, before

adding any data, after adding all Tevatron and LHC data and adding only the Tevatron

and LHC 7 TeV data points. The slight improvement of an already good quantitative

description can be seen. As expected, the agreement of the prediction with LHC8 data,

when only Tevatron and LHC7 data are used, is a non-trivial consistency check of the

whole procedure.12

Given that the constraints from top quark data in a global PDF fit such as NNPDF2.3

are already substantial, we expect even larger constrains in PDF sets based on reduced

11Note that, as shown by Fig. 1, the typical x ranges covered by the theory predictions at LHC 7, 8

and 14 TeV are quite similar, justifying the extrapolation of lower LHC energy data to improve the theory

predictions at higher LHC center of mass energies.12The small change of the χ2 between TEV+LHC data and TEV+LHC7 data is due to statistical fluc-

tuations, reflecting the fact that the 8 TeV data are still not precise enough to provide constraints on the

gluon PDF.

– 13 –

Figure 4. Left plot: the 7 TeV ATLAS measurements of the pT of top quarks, compared to variousPDF sets. Right plot: the reduction of the gluon large-x PDF uncertainties when inclusive top quarkcross-sections are added to the NNPDF2.3 NNLO fit [40].

to precompute Madgraph5 aMC@NLO [46] cross-sections, with the exact NNLO results. Thesame fast grid techniques could also be used to interface directly the very CPU-intensive NNLOcalculations into PDF fits.

Another interesting observable that was discussed is the ratio of cross-sections between 13TeV and 8 TeV [47], where many experimental and theory systematics cancels, providing aclean handle on PDFs. In the specific case of top quark production, the dependence on mt andon the scales is largely canceled in such a ratio, and theory uncertainties are mostly driven bydifferences in the gluon PDF. There are plans to perform these measurements by both ATLASand CMS.

6. Approximate calculations for top pair productionIn addition to exact NLO and NNLO calculations (both fixed order and matched to partonshowers), we also discussed recent progress in approximate calculations in top quark production.In the case of the total cross-section, it has been recently proposed that it is possible to compute arobust estimate of yet unknown higher orders by using known results and exploiting the analyticproperties of the partonic cross-sections in Mellin space. This technique has been successfullyapplied to Higgs production in gluon fusion [48], validated by available NNLO and partialN3LO results, and during the workshop we discussed its extension to an approximate N3LO σttcalculation. An interesting related issue with approximate N3LO calculations is whether NNLOPDFs are sufficient, or if one really needs N3LO PDFs. This problem has been addressed inRef. [49], finding that, interestingly, N3LO are not required for Higgs production, but that theyare needed for tt production. The reason for this is the fact that in top production a larger valueof Bjorken-x is probed that in Higgs production.

For differential distributions, approximate higher-order results can be obtained usingtechniques that stem from the resummation to all orders of terms enhanced in the soft andcollinear limits. For instance, we discussed recent studies [50], where the renormalization groupequations are used to derive approximate NNLO top quark differential distributions includingsemi-leptonic top quark decays computed in the narrow-width approximation. Related earlierstudies include [51]. Previously, various approximations for the NNLO cross-section were alsoavailable [35,52].

7. BSM physics searches with top quarksTop quarks are a crucial ingredient in essentially all scenarios for physics beyond the StandardModel. Their large Yukawa coupling suggest that they could play a major role in understandingthe origin of the electroweak symmetry breaking mechanisms. In addition, the top quarkcontribution to quantum corrections to the Higgs boson mass is at the heart of the hierarchyproblem, and naturalness-based solutions to this problem typically require the presence of toppartners. It is therefore clear that searches for New Physics that involve top quarks in the finalstate are very important at the LHC.

In these searches, SM top quark production is typically the dominant background, andtherefore the recent developments in precision calculations in top physics should certainlyimprove the reach of BSM searchers. For instance, the NNLO calculation of the total cross-section has been used in [53, 54] to improve the bounds on light stop quarks. Another exampleis provided by the fact that PDF uncertainties are one of the dominant modeling systematicsin many searches, specially those that involve invariant masses at the TeV scale, and reducingthese PDF errors, with top quark data in particular, would certainly improve the reach ofthese searches for New Physics [34]. Another important aspect that was emphasized during theworkshop was that BSM searches typically probe top quark production in extreme kinematicalregions, as illustrated schematically in Fig. 5. In particular, BSM searches require goodunderstanding of top quark production in association with many jets or vector bosons, topquark pairs with TeV invariant masses and tt and single top production in association withsubstantial missing ET .

Extreme phase space ttbar: background for searches "

Freya Blekman (IIHE,Vrije Universiteit Brussel)" 3"

more jets/V bosons!

High MET!

Z’--->ttbar!W’--->tb!

H0--->ttbar!H±--->tb!

Ttbar+DM!Single top+DM!

(monotop)!

! !

Top quark compositeness (t*)!

Vector-like quarks (t’/b’) !

ttH!

SM differential & BR measurements !

incl spin correlations!

sGluons!

tt+X resonances

● X is important!

● Width is important

● It gets (almost always) worse at the reconstruction level

Figure 5. Left plot: schematic illustration of the different extreme kinematical regions probed byBSM searches at the LHC with top quarks in the final state (courtesy of F. Blekman). Right plot: thereconstructed mass of a top quark pair mreco

tt in BSM scenarios where a heavy resonance ρ decays into att pair (red histogram) or to other intermediate resonances which in turn decay to top quarks (blue andgreen histograms), from [55].

Another topic that was discussed is that recent LHC results strongly suggest that one shouldadopt new search strategies to look for New Physics. For instance, many searches look for heavyresonances coupled to top quarks by reconstructing the invariant mass of the tt pair and tryingto identify a resonance on top of the SM background. However, in more realistic BSM scenariosthis heavy resonance will instead decay to other BSM states which in turn decay to top quarks,and the peak in tt will disappear, see Fig. 5 for an illustration taken from [55]. This exampleshows that a cross-talk between BSM theorists, theorists involved in precision SM calculationsand experimentalists is essential in order to to maximize the scientific output of the LHC dataanalyses.

AcknowledgmentsWe warmly acknowledge all workshop participants for their enthusiastic contributions and forthe many lively discussions. We are especially grateful to Frederic Deliot and Roberto Chiericifor their help with the organization of the workshop. The work of M. C. was supported bythe German Research Foundation (DFG) via the Sonderforschungsbereich/Transregio SFB/TR-9 “Computational Particle Physics”. The work of A. M. is supported by the UK Science andTechnology Facilities Council [grants ST/L002760/1 and ST/K004883/1]. The work of J. R. wassupported by an STFC Rutherford Fellowship ST/K005227/1 and by the European ResearchCouncil Starting Grant ”PDF4BSM”.

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