Constraining CP violating operators in charged and neutral triple gauge couplings
IIPPP/20/77MCnet-21-01
Constraining CP violating operators in charged andneutral triple gauge couplings
Anke Biek¨otter a,b , Parisa Gregg a,b , Frank Krauss a,b and Marek Sch¨onherr aa Institute for Particle Physics Phenomenology, Durham University, United Kingdom b Institute for Data Science, Durham University, United Kingdom
Abstract
We constrain CP -violating charged and neutral anomalous triple gauge couplings using LHCmeasurements and projections of diboson and VBF V jj production, both with subsequent leptonicdecays. For triple gauge couplings involving W bosons we analyse differential asymmetries andinterpret our results in the SMEFT at dimension-six. For neutral triple gauge couplings, which aredominantly constrained by high transverse-momentum bins, we present the resulting bounds in termsof a general anomalous couplings framework. The observation of the Higgs boson in 2012 [1,2] has been a milestone in the confirmation of electroweaksymmetry breaking (EWSB). Since, apart from fixing the Higgs couplings, the mechanism of EWSBalso predicts the interactions of the electroweak gauge bosons, precise measurements of the triple gaugecouplings (TGCs) play a crucial role in experimentally testing the SM. CP -violating interactions of thegauge bosons are of particular relevance in this regard, since they provide additional sources of CP violation, necessary to describe, for example, electroweak baryogenesis [3–7].In our work, we study CP -odd anomalous triple gauge couplings involving two (charged) W bosons, W W Z and
W W γ , as well as interactions of neutral gauge bosons,
ZZZ , ZZγ and
Zγγ , which arecompletely absent in the SM. For charged anomalous triple gauge couplings, we consider constraints fromthe measurement of
W W → (cid:96)(cid:96) (cid:48) νν [8], W Z → (cid:96) + (cid:96) − (cid:96) ± ν [9], W γ → (cid:96) ± νγ [10], Zjj → (cid:96) + (cid:96) − jj [11] and W jj → (cid:96)νjj production [12]. To describe small deviations from the Standard Model (SM) values of thecharged TGCs in a model-independent fashion, we will use the language of Standard Model Effective FieldTheory (SMEFT) [13–17], where CP -odd SMEFT operators influencing the charged TGCs appear atdimension six. Constraints on these operators have been studied and constrained in Higgs boson [18–23]and diboson production processes [24–27] as well as vector boson scattering [28]. Recently, CP violationin diboson production has also been studied in Ref. [29]. We consider the same experimental inputs, butour analysis differs in the selection of observables sensitive to CP violation, using differential asymmetriesrather than complete differential distributions, reducing both experimental and theoretical systematicuncertainties. Our study provides an independent confirmation of the results found in Ref. [29] usingS HERPA for the generation of both the SM as well as the beyond SM events, and they also serve asindependent validation of the implementation of this sector in S
HERPA .For neutral anomalous triple gauge couplings we consider constraints from the ZZ → (cid:96) and 2 (cid:96) ν final states [30, 31] as well as Zγ → (cid:96)γ and 2 νγ production channels [32, 33]. Due to the dominanceof squared neutral triple gauge coupling (nTGC) contributions compared to the polarization-suppressed(linear) interference with the SM [25,34,35], we investigate their effects on the cross section in the high- p T regime, rather than studying asymmetries. SMEFT [13–17] provides a versatile framework to describe small deviations from the SM, such as thoseinduced by anomalous triple gauge couplings. In the Warsaw basis [15], there are two dimension-six a r X i v : . [ h e p - ph ] M a r perators leading to CP violation in diboson production through a modification of the γW W and ZW W interactions. We can describe them through the effective Lagrangian L = L SM + c ˜ W Λ O ˜ W + c H ˜ W B Λ O H ˜ W B , (1)where L SM is the SM Lagrangian, Λ denotes the new physics scale and the c i are the Wilson coefficientsof the operators O ˜ W = (cid:15) IJK ˜ W Iνµ W Jρν W Kµρ , O H ˜ W B = H † τ I H ˜ W Iµν B µν . (2)The operator O H ˜ W B also affects Higgs-gauge couplings and its Wilson coefficient can thus be constrainedindependently through Higgs sector observables.In the following, we calculate and combine the constraints on the Wilson coefficients c H ˜ W B and c ˜ W from W W , W Z , W γ and VBF
Zjj and
W jj production at the LHC. For each considered channel i , westudy the differential distributions of an angle ζ i which is defined from the triple products or, equivalently,the difference in azimuthal angle of the rapidity-ordered final-state (pseudo-)particles k and l , e.g. ∆ φ kl ∝ sin − (( (cid:126)p k − (cid:126)p l ) z ( (cid:126)p k × (cid:126)p l ) z ). The operators O ˜ W and O H ˜ W B produce modulations in these distributions.As an example, we display the ∆ φ jj distribution for the two tagging jets in Zjj production in Fig. 1. We jj r a t i o w r t S M SM c W = 0.25 c HWB = 2
Figure 1: ∆ φ jj distribution for the Zjj analysis.divide each of these ∆ φ distributions into six pairs of bins using the boundaries ± [0 , , , , , , · π and construct six asymmetries A ij between the number N of events in corresponding bins at positive ornegative ∆ φ , i.e. we compare the number of events in the bin [ − π ,
0] with the number of events in thebin [0 , π ] and so on: A ij = N i, − j − N i, + j N i, − j + N i, + j i = W W, W Z, W γ, Zjj, W jj, j = 1 , . . . , . (3)In the above, N i,j corresponds to number of events in bin j of the ∆ φ distribution for channel i . Theresulting differential asymmetries A ij are defined such that they vanish exactly for the SM and SMbackgrounds, where no CP violation is present. ∗ The study of asymmetries has the advantage thatsystematic uncertainties largely cancel in the ratio and the limits are therefore entirely determined bythe statistical uncertainties. For channels with a signal-over-background ratio smaller than one, we takeinto account the uncertainty from background subtraction as σ bkg A ij = (cid:113) N bkg ij /N sig ij .We generate events at leading order (LO) with S HERPA -2.2.10 [36,37] with the default
NNPDF30 nnlo as 0118 parton distribution function [38] from L
HAPDF
OMIX [40]and parton showered with C
SSHOWER [41]. QED corrections are effected through a YFS soft-photon re-summation [42, 43]. For multi-parton interactions, hadronisation, and subsequent hadron decays we usethe S
HERPA default settings. EFT contributions are generated using the
SMEFTsim model [44] in S
HERPA through its UFO [45] interface [46]. We consider the interference of the SM with the dimension-sixoperator only and neglect contributions from the squares of dimension-six terms.In each channel, we normalize the SM cross section to the experimentally observed cross section andassume identical normalization factors for the SM and the EFT contributions. To take into accountdetector effects, we include a flat detector efficiency which we deduce from the ratio of the predicted ∗ The CP violation present in the SM have been checked to be negligible for the range of observables and coefficientsconsidered in this letter. (cid:15) det = N events, pred / ( σ pred L int ). W W production.
For
W W production, we consider an asymmetry in the sine of the difference of theazimuthal angles φ of the two final state leptons ordered by their pseudorapidity, ζ W W = ∆ φ (cid:96)(cid:96) . We makeuse of the existing R IVET [47] analysis to reproduce the experimental cuts and normalize the S
HERPA cross section to the measured value of σ fid ,EW = 379 . ± . (cid:15) det = 0 . S/B >
1, we can safely neglect the uncertainty from backgroundsubtraction.
W Z production.
For
W Z production, the CP -sensitive observable considered is ζ W Z = ∆ φ Z(cid:96) (cid:48) , where (cid:96) (cid:48) denotes the lepton from the decay of the W boson and Z denotes the reconstructed Z boson fromthe same-flavor-opposite-sign lepton pair. We normalize the S HERPA cross section to the measured valueof σ fid ,EW = 254 . ± . (cid:15) det = 0 .
52. Since the signal-over-background ratio
S/B >
1, we can safely neglect the background contributions.
W γ production
For
W γ production in the (cid:96)νγ final state we define the CP sensitive observable ζ W γ =∆ φ γ(cid:96) , where (cid:96) and γ denote the lepton from the W boson decay and of the photon, respectively. CMS hasperformed an analysis for W γ production at 13 TeV for an integrated luminosity of L = 127 . − [10].Including the decay of the W boson, the analysis has measured a cross section of σ fid = (3 . ± .
16) pb.We implemented the experimental cuts in R
IVET and normalized the cross section after cuts to thisvalue. From the expected number of signal events and the expected cross section, we deduce a detectorefficiency of (cid:15) det = 0 .
59. For
W γ production, the signal-over-background ratio after cuts is
S/B ≈ . e -induced photons, it is difficult to estimate their shape. For this reason, we assume thebackground shape to closely follow the signal shape in ∆ φ γ(cid:96) . Zjj production
In vector boson fusion
Zjj production, CP violation in the ZW W and γW W cou-plings causes modulations in the ∆ φ jj distribution of the η -ordered jets, see Fig. 1. We normalize theS HERPA cross section to the measured value of σ fid ,EW = 37 . ± . (cid:15) det = 0 .
85 for detector effects. Since
S/B ≈ .
59, we consider the uncertainty from backgroundsubtraction using the ∆ φ jj distribution for the background as given in the experimental reference. W jj production
For VBF
W jj production, we again base our analysis on the ∆ φ jj distribution of the η -ordered jets. On top of the baseline selection used in Ref. [12], we apply a stricter cut on the invariantmass of the tagging jets m jj > S/B ≈ .
13. Forthe background, we have generated the dominant QCD
W jj contribution with S
HERPA to obtain theshape. We normalize the event numbers to match the predicted number of total signal and backgroundevents in Ref. [12] rescaled by the luminosity.
Combination.
We combine the constraints on the Wilson coefficients from measurements of the
W W , W Z , W γ , Zjj and
W jj channels in a χ analysis. Since systematic uncertainties cancel out in ourobservables, we do not need to consider correlations between uncertainties of the different channels anddirectly calculate the χ from the differential asymmetries A ij via χ = (cid:88) i,j ( A ij − . ) σ A ij , i = W W, W Z, W γ, Zjj, W jj, j = 1 , . . . , , (4)where σ A ij denotes the combined statistical uncertainty from signal and background on the asymmetryin bin j of channel i .We present the expected results for LHC Run II with an integrated luminosity of L int = 139 fb − aswell as prospects for the high luminosity LHC with an integrated luminosity L int = 3000 fb − in Fig. 2.The strongest constraints result from W γ production for c H ˜ W B and from the
Zjj and
W jj channels3or c ˜ W . Our bounds approximately agree with those presented in Ref. [29] † . Some differences occur dueto the inclusion of detector inefficiencies. For the W γ channel, we benefit from being able to recast anexisting 13 TeV analysis rather than relying on assumptions for the cuts. Therefore, the cross sectionused for this channel is a factor 10 smaller in our analysis than assumed in Ref. [29].Our limit on c H ˜ W B is much stronger than the bound resulting from Higgs observables. At 3000 fb − luminosity the expected limits are | c H ˜ W B | / Λ < . − from Higgs WBF+ γ production [23] and | c H ˜ W B | / Λ < . − from standard Higgs production processes [20] respectively compared to | c H ˜ W B | / Λ < .
04 TeV − for this analysis of diboson observables. A fit combination of Higgs and diboson observ-ables could in turn further improve the limits on other Wilson coefficients currently constrained fromHiggs observables, c H ˜ G , c H ˜ W and c H ˜ B . The Wilson coefficient of the operator O ˜ W is constrained to | c ˜ W | / Λ < .
02 TeV − in our fit. High-luminosity LHC projections for diboson plus vector boson scat-tering data using distributions up to high- p T instead of actual CP -sensitive observables find competitiveconstraints [28], further highlighting the necessity to combine fits of all available LHC data sets. c HWB / [TeV ]0.500.250.000.250.50 c W / [ T e V ] combinedZjjWjj WW W int = 139 ifb c HWB / [TeV ]0.100.050.000.050.10 c W / [ T e V ] combinedZjj Wjj WW W int = 3000 ifb Figure 2: Combination of the 95% CL limits from
W W , W Z , W γ and
Zjj production after LHC Run II( L int = 139 fb − , left) and after the HL-LHC ( L int = 3000 fb − , right). The limits from W Z productionare too weak to be visible in the plots.
Neutral triple gauge couplings are absent in the SM at LO. Therefore, the observation of these couplingswould be a clear hint for physics beyond the SM [48]. The most general parametrization of nTGCs in ZZ and Zγ production is given by [49], cf. also [34, 50, 51], L = L SM + eM Z (cid:20) − [ f γ ( ∂ µ F µβ ) + f Z ( ∂ µ Z µβ )] Z α ( ∂ α Z β ) + [ f γ ( ∂ σ F σµ ) + f Z ( ∂ σ Z σµ )] (cid:101) Z µβ Z β − [ h γ ( ∂ σ F σµ ) + h Z ( ∂ σ Z σµ )] Z β F µβ − [ h γ ( ∂ σ F σρ ) + h Z ( ∂ σ Z σρ )] Z α (cid:101) F ρα − M Z (cid:110) h γ [ ∂ α ∂ β ∂ ρ F ρµ ] + h Z [ ∂ α ∂ β ( (cid:3) + M Z ) Z µ ] (cid:111) Z α F µβ + 12 M Z (cid:110) h γ [ (cid:3) ∂ σ F ρα ] + h Z [( (cid:3) + M Z ) ∂ σ Z ρα ] (cid:111) Z σ (cid:101) F ρα (cid:21) . (5)Non-zero coefficients f V , h V and h V lead to CP -violating interactions, while the coefficients f V , h V and h V parametrize CP -conserving ZZZ , ZZγ and
Zγγ interactions. In the SM, all h i and f i are zero attree level. At the one-loop level, however, the CP -conserving couplings f , h and h , receive non-zerocontributions with relative sizes at the order of O (10 − ) [52].In contrast to charged TGCs, neutral TGCs can currently only be constrained to a regime where thequadratic terms clearly dominate over the linear interference terms with the SM, which are suppressedby the allowed polarizations of the gauge bosons. As a result, bounds on CP -violating neutral triplegauge couplings (nTGCs) stem primarily from their effect on the cross section in the high- p T regime † Notice that our paper has a sign difference for the operator c H ˜ WB with respect to Ref. [29] and Ref. [11]. We havevalidated our results by detailed comparison with MadGraph, with identical results. The one-parameter limits presentedare not affected by the sign change. CP -sensitive observables [25, 34, 35]. In this section, we will therefore studythe enhancement of relevant cross sections in high-momentum bins of kinematic distributions ratherthan CP asymmetries. In particular, we will study the high- p T regime of the distributions of p (cid:96)(cid:96)T in ZZ production as well as E T,γ in Zγ production. Bounds on nTGCs have previously been discussed forthe LHC [25, 34, 35, 53] as well as for future lepton [54, 55] and proton colliders [56–58]. Since both thebounds on the coefficients of CP -violating interactions and their CP -conserving counterparts ( f V ↔ f V , h V ↔ h V , h V ↔ h V ) result from their quadratic effect on the cross section in the high- p T regime, theirlimits are typically very similar.Neutral triple gauge couplings do not appear at the dimension-six level in the SMEFT. They are,however, induced at dimension-eight [53] ( f V , f γ , h V , h Z ) or even higher dimension. While an interpre-tation of nTGCs in SMEFT at dimension-eight is therefore possible, the clear dominance of the quadraticterms over the dimension-eight interference terms renders the interpretation cumbersome and possiblyflawed. Consequently, we will rely on the parametrization given in Eq. (5).Events for the analysis of neutral anomalous gauge couplings are generated at leading order usingthe native SM+AGC model in S
HERPA -2.1.1 [36] as well as an implementation in a UFO model [37, 46, 59].Event generation includes both the suppressed and mostly negligible interference with the SM model aswell as the squared nTGC contributions. ZZ production. We study ZZ production in its leptonic 4 (cid:96) [30] and 2 (cid:96) ν [31] final states. Themeasured cross sections in the fiducial regions of these channels are σ (cid:96) = (46 . ± .
4) fb [30] and σ (cid:96) ν = (25 . ± .
7) fb [31], respectively. In both cases, we use the p (cid:96)(cid:96)T distributions to constrain thenTGC; in the 4 (cid:96) final state we use the two leptons of the leading reconstructed Z boson. To facilitatedirect comparison with published data, we employ the binning used by the experimental collaborationsfor their luminosity projections.In our event generation, we include the LO gg and qq initial state contributions for ZZ production.The effect of nTGCs is, however, only included for the qq intial state which makes up for about 90% ofthe total number of events. NNLO QCD and NLO EW corrections for the events are included throughbin-by-bin k factors, assuming the same values for SM and BSM contributions. These are deduced fromthe ratio of the LO results with respect to the most precise S HERPA prediction available. The totalnumber of events in each bin i is given by N S HERPA i = N qqi + N ggi = (cid:15) det i L int ( σ qq, NLO i + 1 . σ ggi ), wherethe gg contribution is corrected by a relative k factor of 1 .
67. Detector effects are accounted for throughbin-by-bin detector efficiency factors (cid:15) det i for the 4 (cid:96) final state (ranging between 0 .
57 and 0 .
69) while weuse a global detector efficiency of (cid:15) det = 0 .
57 for the 2 (cid:96) ν analysis.luminosity [ fb − ] | f γ | × | f Z | ×
139 11 . . . . . . . . . . ZZ → (cid:96) and ZZ → (cid:96) ν analyses atdifferent luminosities. The limits on the parameters f V which lead to CP -conserving interactions areequivalent to those on their CP -violating counterparts. In the two bottom rows, we present the limitsassuming that the relative systematic uncertainties in each bin have been halved with respect to thevalue quoted by the experimental collaborations at 36 . − .To set limits on the nTGCs, we perform a χ analysis for each bin in the two available p (cid:96)(cid:96)T distributions, χ = (cid:88) i ∈ bins ( N data i − N pred i ) N data i + ( σ syst i ) , (6)where N data i and N pred i denote the number of observed and predicted events in each bin and σ syst i is theirsystematic uncertainty. For both analysis channels, the constraints on nTGCs stem almost entirely fromthe last bin, i.e. p (cid:96)(cid:96)T ∈ [555 , (cid:96) final state and p (cid:96)(cid:96)T ∈ [350 , (cid:96) ν final state.To validate our analysis, we have explicitly checked that we can reproduce the limits on f Vi presentedby the experimental collaborations [30, 31] for a luminosity of 36 . − at the 15% level. Deviations5rom those limits can be fully explained by the use of different Monte Carlo generators and the fact thatwe only know the global detector acceptance rather than a bin-by-bin value for the 2 (cid:96) ν final state.Combining the limits from the 4 (cid:96) and 2 (cid:96) ν final states for a luminosity of 3000 fb − , we find 95 % CLbounds of | f γ | < . × − , | f Z | < . × − , (7)for the parameters inducing CP -violating interactions. Since the linear interference contributions are notstatistically relevant, we display the limit on the absolute values of the parameters instead of presentingseparated upper and lower 95 % CL limits. We collect projected limits at different luminosities in Tab. 1.As expected, the limits on the parameters f V which lead to CP -conserving interactions are equivalentto those of its CP -violating counterparts f V . Our combined 139 fb − limits approximately agree withthose found by CMS for LHC Run-II in the 4 (cid:96) final state [60], which however draws most of its sensitivityfrom an overflow bin, m ZZ > (cid:46)
20 %. We generally avoid including theoverflow in our last bins, however, to make sure that all considered events lie in a kinematic regime forwhich the detector is well understood. In addition, using a constrained last bins circumvents potentialissues when translating the limits to other frameworks such as EFTs. Zγ production. We study Zγ production in the leptonic 2 (cid:96)γ [32] and 2 νγ final states [33] to constrainthe CP -odd interactions induced by h V and h V , compare Eq. (5). The measured inclusive cross sectionfor 2 (cid:96)γ final state is σ (cid:96)γ = (1065 . ± .
5) fb [32]. For the analysis of the 2 νγ final state which vetoesadditional jets, the measured cross section is σ νγ = (52 . ± .
8) fb [33]. We assume a detector efficiencyof (cid:15) det2 (cid:96)γ = 0 .
54 for the 2 (cid:96)γ channel and (cid:15) det2 νγ = 0 .
89 for the 2 νγ channel. NNLO QCD and NLO EWcorrections are again included through bin-by-bin k factors by rescaling to the predictions in Refs. [32,33].To calculate and combine the limits from Zγ , we again add up χ for each bin in the E T,γ distribution,see Eq. (6), using the binning given in the corresponding experimental references excluding overflow bins.Our last bins, which have the greatest sensitivity to the nTGCs, range from E T,γ ∈ [500 , (cid:96)γ and E T,γ ∈ [600 , νγ analysis. As we will point out below, including the overflowin the last bin has a severe impact on the limits on h V . To validate our analysis, we have explicitlychecked that we can reproduce the expected limits of the analysis of the 2 νγ final state at a luminosityof 36 . − [33] when including the overflow in the last bin.Combining the limits from the 2 (cid:96)γ and 2 νγ final states for a luminosity of 3000 fb − , we find 95 % CLbounds of | h γ | < . × − , | h Z | < . × − , | h γ | < . × − , | h Z | < . × − , (8)for the CP -odd nTGCs. These values assume the same relative systematic uncertainties as in the ex-perimental references at 36 . − and 139 fb − . Including the overflow in the last bin, the limits on h V tighten by ∼
20 %. On the other hand, the limits on h V are much more severely affected; they areapproximately halved when including the overflow in the last bin. This implies that care has to be takenwhen translating limits based on an analysis including the overflow bin such as Ref. [33] into, for instance,an EFT framework. We collect the limits for other luminosities in Tab. 2. Since for higher luminositiesand a fixed binning the uncertainty on the last bin quickly becomes dominated by systematic effects, wealso present limits assuming systematic uncertainties are reduced by a factor of two. Because the limitsluminosity [ fb − ] | h γ | × | h Z | × | h γ | × | h Z | ×
139 3 . . . . . . . . . . . . . . . . . . . . Zγ → (cid:96)γ and Zγ → νγ analyses atdifferent luminosities. In the two bottom rows, we present the limits assuming that the relative system-atic uncertainties in each bin have been halved with respect to the value quoted by the experimentalcollaborations. 6n CP -even nTGCs are roughly equivalent to those on their CP -odd counterparts we do not presentthem explicitly here. We have studied the constraints on CP -odd anomalous triple gauge couplings from diboson production.For the TGCs involving W bosons, we have analysed differential asymmetries in CP -sensitive observ-ables based on ∆ φ and present our results in the SMEFT framework at dimension-six. Marginalizingover the second Wilson coefficient, we can constrain the coefficients to | c H ˜ W B | / Λ < .
04 TeV − and | c ˜ W | / Λ < .
02 TeV − at 3000 fb − . The strongest limits stem from the analysis of W γ , W jj and
Zjj production. The improved limits on the coefficient c H ˜ W B with respect to limits resulting from Higgsobservables, motivates a combination of Higgs, vector boson scattering and diboson data for a combinedfit of CP -violating operators.To constrain neutral triple gauge couplings, we combined the bounds from the leptonic decay channelsof ZZ and Zγ production. The most severe limits are obtained from the high- p T regimes of differentialdistributions instead of CP -sensitive observables due to vanishingly small SM–New Physics interferenceterms. The resulting combined limits on CP -odd interactions at 3000 fb − are | f Z | < . × − , | f γ | < . × − from ZZ production and | h γ | < . × − , | h Z | < . × − , | h γ | , | h Z | < . × − from Zγ production. Limits on h V are significantly tighter when including the overflow above ∼ CP -odd anomalous triple gauge couplings for futureruns of the LHC and thereby provided bounds on additional sources of CP -violation in the SM. Acknowledgements
PG, FK and MS are supported by the UK Science and Technology Facilities Council (STFC) under grantST/P001246/1. AB gratefully acknowledges support from the Alexander-von-Humboldt foundation asa Feodor-Lynen Fellow. FK and MS are acknowledging support from the European Union’s Horizon2020 research and innovation programme as part of the Marie Sklodowska-Curie Innovative TrainingNetwork MCnetITN3 (grant agreement no. 722104). MS is funded by the Royal Society through a Uni-versity Research Fellowship (URF \ R1 \ \ R1 \ References [1] G. Aad et al., ATLAS,
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