Anomalous couplings in WZ production beyond NLO QCD
Francisco Campanario, Robin Roth, Sebastian Sapeta, Dieter Zeppenfeld
AAnomalous couplings in WZ production beyondNLO QCD
Robin Roth ∗ † Institute for Theoretical Physics, KIT, 76128 Karlsruhe, GermanyE-mail: [email protected]
Francisco Campanario
Theory Division, IFIC, University of Valencia-CSIC, E-46980 Paterna, Valencia, SpainE-mail: [email protected]
Sebastian Sapeta
CERN PH-TH, CH-1211, Geneva 23, SwitzerlandE-mail: [email protected]
Dieter Zeppenfeld
Institute for Theoretical Physics, KIT, 76128 Karlsruhe, GermanyE-mail: [email protected]
We study WZ production with anomalous couplings at ¯ n NLO QCD using the LoopSim method incombination with the Monte Carlo program
VBFNLO . Higher order corrections to WZ productionare dominated by additional hard jet radiation. Those contributions are insensitive to anomalouscouplings and should thus be removed in analyses. We do this using a dynamical jet veto basedon the transverse energy of the QCD and EW final state particles. This removes jet dominatedevents without introducing problematic logs like a fixed p T jet veto. Fourth Annual Large Hadron Collider Physics13-18 June 2016Lund, Sweden ∗ Speaker. † KA-TP-32-2016 c (cid:13) 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/ a r X i v : . [ h e p - ph ] D ec nomalous couplings in WZ production beyond NLO QCD Robin Roth
1. Introduction
The production of two heavy vector bosons is an interesting process, as it allows to studythe interactions between the gauge bosons. Leptonic decays of the vector bosons can be usedto discriminate backgrounds and get precise measurements of the kinematics. Searches for newphysics include new resonances decaying to vector boson pairs and changes to their couplings dueto new particles in loops. Those can appear in tails of distributions or as modifications in angulardistributions sensitive to spin. To measure diboson production and search for deviations from theStandard Model (SM) high center of mass energies and high luminosities are required, such that themost recent LHC upgrades promise to enhance those analyses.In this contribution, we study WZ production as a representative diboson production process.We calculate NLO QCD corrections to WZ and WZj production with VBFNLO and combine themto get ¯ n NLO accuracy using the LoopSim approach [1]. This improves the prediction especially forhigh- p T vector bosons. Recently a calculation of the inclusive cross section of WZ production atNNLO QCD was reported in Ref. [2], but there are no differential distributions available yet. We study Anomalous Couplings (AC) using an Effective Field Theory (EFT) approach. Thisallows to parametrize deviations from the Standard Model (SM) interactions, especially in triple andquartic gauge couplings in a general way without choosing a specific model. Effects of AC are mostvisible in the region of high invariant-mass diboson pairs with high transverse momentum of thefinal state particles. In particular in the high- p T region, the LoopSim approach should approximatethe full NNLO corrections closely.WZ production has been measured at the LHC in several decay channels. The fully leptonicdecay, as studied in Ref. [3, 4, 5, 6, 7], has little background, but at the same time the smallest crosssection. Semi-leptonic final states, [8, 9], have a larger cross sections but suffer from backgroundsdue to top production and single-vector-boson + jets. Measuring the cross section allows to setlimits on anomalous triple gauge couplings, as many of the analyses do. For details on dibosonmeasurements see also the contributions by S.L. Barnes and N. Woods in these proceedings.
2. Calculational setup
For the simulation, we use
VBFNLO [10, 11, 12] in combination with LoopSim [1]. The setupis comparable to previous work with LoopSim on WZ [13], WW [14] and ZZ production [15].LoopSim generates a merged sample of WZ@NLO and WZj@NLO [16] to give us WZ@ ¯ n NLO.For the study of AC, we are interested in phase space regions with high transverse momentum andhigh invariant mass of electroweak particles. These can get large contributions from additionalQCD radiation of O ( α s ln p Tjet / m Z ) , which are included in LoopSim. Compared to the full NNLOcalculation, LoopSim misses the finite 2-loop contributions. Those are expected to be on the levelof a few percent, since they are suppressed by α and are not enhanced, like some real emissioncontributions. Due to the missing contributions the prediction of the total cross section, the low- p T phase space region and the scale dependence is only NLO. On NNLO QCD calculations of diboson production see the contribution by S. Kallweit, “NNLO di-boson produc-tion.” nomalous couplings in WZ production beyond NLO QCD Robin Roth
To parametrize AC, we use the set of dimension-6 operators based on the HISZ basis [17] asupdated in Ref. [18]. They extend the SM via L = L SM + ∑ i f i Λ O i . Assuming C and P invariance,only three operators contribute to the WWZ vertex: O W = (cid:0) D µ Φ (cid:1) † (cid:98) W µν ( D ν Φ ) , (2.1) O B = (cid:0) D µ Φ (cid:1) † (cid:98) B µν ( D ν Φ ) , (2.2) O WWW = Tr (cid:104) (cid:98) W µν (cid:98) W νρ (cid:98) W µρ (cid:105) . (2.3)We focus on the O W operator for this work. It is a suitable representative for AC as it leads to aterm with non-SM Lorentz structure in the WWZ vertex. To get meaningful limits on AC, onehas to consider a complete set of operators, which affect a given observable, including correlationsbetween operators.Diboson production processes are competitive in limiting dimension 6 operators and aretherefore included in global fits of AC limits, like Refs. [19, 20, 21]. Our values used for thecouplings are in the allowed region of Ref. [19] and represent typical values current measurementsare sensitive to. Effective Field Theory (EFT) for triple gauge couplings assumes an expansion in f Λ . Thisdepends on both the coupling of new physics as well as its energy scale. The expansion is only validif the scale of the considered observable is smaller than the new physics scale entering Λ .For high invariant masses, the EFT operators violate unitarity of the S-matrix. This is a signthat the EFT approach is no longer valid and should be replaced by a UV complete model. To stillget physical predications, one can apply a unitarization procedure. We use the form factor FF = (cid:18) + m WZ Λ (cid:19) -n , with Λ FF = = . (2.4)The value for the form factor scale is determined with the VBFNLO form factor tool [22], such thatthe operator does not lead to unitarity violation in 2 → Λ FF is fixed,such that this description leaves no free parameter in the unitarization scheme. For most plots, wewill focus on phase space regions significantly below Λ FF where neither the form factor nor mostunitarization procedures would have a visible effect.Even below the scale of unitarity violation, there is an ambiguity in how to make predictionsusing an EFT. In the calculation of the squared matrix element |M| , there are interference termsbetween the SM and AC as well as purely AC terms. If one considers an amplitude with contributionsfrom AC operators of dimension 6 and dimension 8, the terms are: M = M SM + M d = (cid:124) (cid:123)(cid:122) (cid:125) / Λ + M d = (cid:124) (cid:123)(cid:122) (cid:125) / Λ + O ( Λ − ) (2.5) |M| = |M SM | (cid:124) (cid:123)(cid:122) (cid:125) / Λ + M ∗ SM M d = (cid:124) (cid:123)(cid:122) (cid:125) / Λ + (cid:12)(cid:12) M d = (cid:12)(cid:12) (cid:124) (cid:123)(cid:122) (cid:125) / Λ + M ∗ SM M d = (cid:124) (cid:123)(cid:122) (cid:125) / Λ + (cid:12)(cid:12) M d = (cid:12)(cid:12) (cid:124) (cid:123)(cid:122) (cid:125) / Λ + O ( Λ − ) (2.6)2 nomalous couplings in WZ production beyond NLO QCD Robin Roth
We include both the M ∗ SM M d = and the (cid:12)(cid:12) M d = (cid:12)(cid:12) term in our calculation. By naive powercounting, one would assume that the latter should be considered simultaneously with dim-8 operators,that contribute via M ∗ SM M d = . This is in general not the case because the SM amplitude issuppressed by the weak coupling, such that (cid:12)(cid:12) M d = (cid:12)(cid:12) can naturally be larger than M ∗ SM M d = .Besides this size argument, there are also practical reasons to include the |M AC | term. Withoutit, one can generate (unphysical) negative cross sections when negative interference exceeds the SMcontribution.To be independent of this ambiguity, one can restrict oneself to phase space regions where thesquared term is not relevant. Based on the sign dependence of the interference, we will study inwhich phase space regions both terms contribute in section 3.2.
3. Numerical results
We consider the LHC at run 2 with pp collisions at 13 TeV. The jets are clustered using theanti- k t algorithm [23] with a cone radius of R = .
4. To simulate typical detector acceptance, weimpose a minimal set of inclusive cuts p T l > p T j > / E T > | y j | < . | η l | < . R l j > . > m ll > , (3.1)where the m ll cut is applied only to same-flavor leptons with opposite sign coming from the Z boson.We consider decays W → e ν e , Z → µ µ . Adding the other leptonic final states increases thenumber of expected events by a factor of 4. For the renormalization scale µ R and factorization scale µ F , we use µ = H T = (cid:32) ∑ partons p T , i + ∑ W , Z (cid:113) p T , i + m i (cid:33) . (3.2)The theoretical uncertainty is estimated using a simultaneous variation of the two scales by afactor of 2: µ R = µ F = { . , } µ . We use the default values set in VBFNLO 3.0 for electroweakconstants and NNPDF23 [24] for the parton distribution functions. ¯ n NLO QCD
Results for WZ production at ¯ n NLO QCD using Loopsim were first presented in Ref. [13].As shown there, the corrections due to ¯ n NLO on top of NLO QCD can be sizeable. A typicalelectroweak observable, like the p T of the hardest lepton ( p Tl,max ), is enhanced by about 25% at300 GeV. Changes are substantially larger for observables sensitive to extra radiation. For H T,jets ,the correction is a factor of 5 at 1 TeV. These distributions are shown in fig. 1. In both cases, thecorrections are outside of the scale variation. The factor 4 is not exact, because of small corrections due to the not-ideal reconstruction in states with identicalflavors and the Pauli interference effect. nomalous couplings in WZ production beyond NLO QCD Robin Roth − − d σ / d p T l , m a x /f b / G e V µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } SM (NLO)SM (nNLO)
50 100 150 200 250 300 p T l,max / GeV1.01.2 σ / S M N L O − − − − d σ / d H T j e t s /f b / G e V µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } SM (NLO)SM (nNLO)
200 400 600 800 1000 H T jets / GeV24 σ / S M N L O Figure 1:
The p T of the leading lepton and H T,jets are shown for WZ production at NLO (dashed) and¯ n NLO QCD (solid). Corrections are typically below 25% as seen on the left for p Tl,max , but can be huge inobservables sensitive to additional emissions, for example they reach a factor of 5 in H T,jets at 1 TeV. Thescale variation is given as a band for NLO (green) and ¯ n NLO (blue). For ¯ n NLO, also the variation of theLoopSim clustering parameter R LS is indicated as a band. Its influence is small for most observables andhighlights phase space regions sensitive to details of the clustering. ¯ n NLO QCD
For AC, we include both the M ∗ SM M AC interference term as well as the |M AC | term, asdiscussed in section 2.2. The interference term is sensitive to the sign of the AC, while the squaredterm is not. Which of the two terms dominated can thus be seen in distributions by looking fordependence on the coupling sign.To show the typical effect of AC, we consider p Tl,max at NLO QCD in fig. 2. For p Tl,max andthe chosen AC values, at around 150 GeV, the destructive interference is maximal, while above300 GeV, the |M AC | term dominates. The interference region gives access to the sign.The corrections at ¯ n NLO shown in fig. 1 are of comparable size to those due to AC. Therefore,an analysis based on a prediction at NLO QCD for the SM might mistake a deviation for a detectionof AC, while a prediction at higher order in QCD might match the measurement. Figure 3 showsa comparison of SM ¯ n NLO and AC NLO that are of similar size. With
VBFNLO and LoopSim,predictions for AC can also be made at ¯ n NLO accuracy. The ¯ n NLO / NLO K-factor depends on thespecific value of the anomalous coupling, such that extrapolating the SM K-factor to AC predictionsgives inaccurate results. This can be seen in fig. 4.
In Ref. [25], we suggested a dynamical jet veto to improve the sensitivity to AC in WZjproduction. We use this veto and study its effect on LoopSim corrections. AC effects typicallygrow with the invariant mass or momentum transfer at triple gauge vertices. To enhance their signal,4 nomalous couplings in WZ production beyond NLO QCD
Robin Roth − − d σ / d p T l , m a x /f b / G e V µ = 2 ± µ (NLO)FW = -5FW = -3FW = +10SM (NLO)
50 100 150 200 250 300 p T l,max / GeV1.01.21.4 σ / S M N L O − − − − − d σ / d p T l , m a x /f b / G e V µ = 2 ± µ (NLO)FW = -5FW = -3FW = +10SM (NLO) p T l,max / GeV5 σ / S M N L O Figure 2:
The effect of the AC operator O W is shown on the p T of the leading lepton at NLO QCD fordifferent regions of p T . The effect grows with p T , such that searches for AC are mostly focused in the high- p T bins of distributions where an enhancement of the SM cross section by a factor of 5 or more is possible (right).The chosen AC values have interferences with the SM most prominent at 150 GeV (left).
50 100 150 200 250 300 p T l,max / GeV10 − − d σ / d p T l , m a x /f b / G e V µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = -5FW = -3FW = +10SM (NLO)SM (nNLO)
50 100 150 200 250 300 p T l,max / GeV1.01.5 σ / S M N L O σ stat µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5FW = -3SM (NLO)SM (nNLO)
Figure 3:
On the left the transverse momentum of the hardest lepton is shown. The right shows the sameobservable, normalized to the SM prediction at NLO QCD. As shown in fig. 1, the ¯ n NLO corrections are onthe order of 25%. Non-vanishing AC can change the cross section by the same amount. Colored dashed linesshow the distribution for AC at NLO QCD, which (depending on the bins considered) give the same value asthe SM ¯ n NLO prediction. For a AC analysis, also all QCD corrections have to be taken into account, leadingto the solid colored lines for AC at ¯ n NLO QCD. nomalous couplings in WZ production beyond NLO QCD Robin Roth
100 200 300 400 500 600 p T l,max / GeV1.01.21.4 n N L O / N L O µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5FW = -3SM (NLO)SM (nNLO)
Figure 4:
The ratio ( d σ ¯nNLO / d σ NLO ) SM , AC for p Tl,max is shown. This K-factor depends significantly on thevalue of the anomalous coupling, ranging from 1.1 to 1.3 for the bin at 600 GeV. Therefore, AC can not beaccurately described by rescaling an AC prediction at NLO with a SM ¯ n NLO/NLO K-factor. the focus is on high-invariant mass boson pairs and high transverse momentum bosons/leptons inthe final state. When a high- p T vector boson is required, this occurs about half of the time due torecoil against a jet (instead of the second vector boson). To reduce those events, one introduces a jetveto. A traditional fixed- p T jet veto rejects all events with additional jets above a certain threshold.This introduces logarithms of the veto scale, which need to be resummed. Also this veto cuts awayrelevant phase space, since in very-high invariant-mass regions (for example m WZ = x jet = ∑ jets E T , i ∑ jets E T , i + E T , W + E T , Z , where E T = E | (cid:126) p t || (cid:126) p | . (3.3)The definition of E T here differs from the one chosen in Ref. [25], where m T = (cid:112) m + p T2 wasused instead. At small p T , the latter is dominated by the mass and thus leads to small x jet valuesfor inclusive samples, while E T generates a broader distribution also in the low- p T region and leadsto better discrimination between SM and AC contributions. In the high- p T region or for masslessparticles, these definitions become identical: m T = E T = p T .In fig. 5, we show the x jet distribution at NLO and ¯ n NLO QCD for the SM as well as for twoexemplary AC values at ¯ n NLO QCD. The ratio to the SM NLO prediction shows a non-flat effectof the ¯ n NLO corrections, enhancing large x jet values. AC contribute at small x jet values. Vetoing x jet > . nomalous couplings in WZ production beyond NLO QCD Robin Roth d σ / d x j e t /f b µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5SM (NLO)SM (nNLO) x jet σ / S M N L O d σ / d x j e t /f b µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5SM (NLO)SM (nNLO) x jet , boosted1.01.5 σ / S M N L O Figure 5: x jet as defined in eq. (3.3) for inclusive and boosted ( p TZ >
200 GeV ) cuts. As visible especially inthe boosted case, there are two relevant phase space regions around small x jet and for x jet ≈ .
5. The latter isnot sensitive to AC, such that the AC analysis should focus on the region below x jet = . . The veto only induces modest logarithms proportional to ln ( x jet ) = ln ( . ) and offers analternative to a fixed- p T veto without the need for resummation. ¯ n NLO is a good testing ground forjet vetos, as all terms with potentially large logarithms are included. Jet veto studies at NLO are notsufficient as they miss the two-jet final state, which is dominant in some phase space regions.Figure 6 shows the p T of the hardest lepton when an additional cut based on x jet is introduced.The veto is designed to cut away jet-dominated events while allowing harder radiation than atraditional fixed jet veto would, especially in the tails of distributions. The veto reduces the ¯ n NLOcorrections. Instead of an increase of 25%, we see a decrease of the cross section by up to 10%. Bycutting away the hard jet events, it also increases the sensitivity to AC.In fig. 6 scale variation bands are given at NLO and ¯ n NLO. Those bands are not a reliableuncertainty estimate, since with jet vetoes the scale dependence is artificially reduced. For anextended discussion and possible better estimates see e.g. Ref. [26]. Besides the scale variationbands, we also show a band for the assumed statistical error. This is a rough estimate based on300 fb − of data in 20 GeV bins. For extrapolation from one combination of lepton families inthe decays of W and Z bosons to all 4 possibilities, we assume a factor 4. In final states such as µ + ν µ µ + µ − , there are two different combinations possible for the reconstruction of the Z boson.We neglect corrections due to imperfect reconstruction and to identical particle effects in that case.Considering ¯ n NLO corrections to different observables, we find that SM and AC receivecorrections with different shapes, such that a description of AC that is based on LO or NLO andrescaled with SM K-factors is not sufficient. In fig. 7, the ¯ n NLO corrections to x jet are shown forthe SM and different AC values. They are identical (within the simulation uncertainty), such thatpotentially a K-factor binned in x jet could describe AC beyond NLO QCD.7 nomalous couplings in WZ production beyond NLO QCD Robin Roth
50 100 150 200 250 300 p T l,max / GeV, x jet < σ / S M N L O σ stat µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5FW = -3SM (NLO)SM (nNLO)
50 100 150 200 250 300 p T l,max / GeV, x jet < σ / S M N L O σ stat µ = 2 ± µ (NLO) µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -5FW = -3SM (NLO)SM (nNLO)
Figure 6:
The effect of anomalous couplings in combination with a jet veto is shown for the cuts x jet < . x jet < .
4. Scale variation bands are given at NLO and ¯ n NLO. An estimate of the statistical uncertainty isgiven as a grey band, for which an integrated luminosity of 300 fb − is assumed as well as a factor 4 for alllepton flavor combinations in the decays. x jet n N L O / N L O µ = 2 ± µ (nNLO) R LS = { } FW = +10FW = -3FW = -5SM (NLO)SM (nNLO)
Figure 7:
The K-factor for x jet of ¯ n NLO compared to NLO is shown for the SM and two values of the O W coupling. The change of ¯ n NLO effects visible in fig. 5 can be reduced to their dependence on x jet . DifferentAC values show similar x jet K-factors and one could thus approximate ¯ n NLO effects by correcting with theshown K-factor. The fluctuations visible in this plot are due to Monte Carlo statistics. nomalous couplings in WZ production beyond NLO QCD Robin Roth
4. Conclusions
We presented a calculation of WZ production at the LHC at ¯ n NLO QCD including AnomalousCouplings (AC) using VBFNLO in combination with LoopSim.To enhance the sensitivity to AC, we use a jet veto based on x jet , as defined in eq. (3.3). Thisreduces the large non-AC contribution where a high- p T jet recoils against a vector boson. The x jet cut improves the sensitivity to anomalous couplings without introducing large logarithms, as isexpected for the traditional fixed- p T jet veto. Furthermore, the x jet veto scales with the hardness ofthe event, such that we include more phase space in the tails of the distribution. Thereby the x jet cutpreserves the region sensitive to AC also at high p TZ .While currently most limits on AC are based on the high- p T tails of distributions, we suggest toalso study the interference region. Since high precision NNLO calculations for vector boson pairproduction are now becoming available also for distributions [27], the theoretical uncertainties inthe interference regions will soon be small enough for a meaningful analysis. This double analysishas the advantage of being sensitive to new physics from both strong coupling (large deviations inthe high energy tail) as well as to intermediate coupling physics at lower energy scales, where alsoelectroweak corrections are still expected to be modest.The dominant kinematical effects of corrections are already present at NLO QCD. Thus,exploratory analyses for AC measurements can be performed with NLO programs. For full dataanalysis, however, the higher precision of NNLO calculations will ultimately be necessary. Acknowledgments
FC has been partially supported by the Spanish Government and ERDF funds from the EuropeanCommission (Grants No. FPA2014-53631-C2-1-P , FPA2014-57816-P, and SEV-2014-0398) RR issupported by the Graduiertenkolleg “GRK 1694: Elementarteilchenphysik bei höchster Energie undhöchster Präzision.”
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