A parton-level analysis exploring potential manifestations of new physics phenomena beyond the Standard Model in triboson production processes is presented. In the context of Standard Model Effective Field Theories, the sensi- tivity to anomalous kinematic effects stemming from the presence of dimension-six operators is evaluated. The results provide valuable insights into the electroweak sector of the Standard Model and potential indications of new physics

Tarricone, C.

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DOI 10.1393/ncc/i2024-24084-1Colloquia: IFAE 2023IL NUOVO CIMENTO 47 C (2024) 84Impact of dimension-six EFT operators on triboson processesat the LHCp˚qC. Tarriconep1qp2qp˚˚qp1q INFN, Sezione di Torino - Torino, Italyp2q Dipartimento di Fisica, Università degli Studi di Torino - Torino, Italyreceived 13 February 2024Summary. — A parton-level analysis exploring potential manifestations of newphysics phenomena beyond the Standard Model in triboson production processesis presented. In the context of Standard Model Effective Field Theories, the sensi-tivity to anomalous kinematic effects stemming from the presence of dimension-sixoperators is evaluated. The results provide valuable insights into the electroweaksector of the Standard Model and potential indications of new physics.1. – IntroductionThe Standard Model Effective Field Theory (SM-EFT) framework provides a de-scription of the effects of new physics via higher-dimensional operators. The SM-EFTLagrangian expands upon the SM, introducing operators modifying the scattering matrixamplitudes, leading to observable event yields. The contribution in the Lagrangian ofeach dimension-n EFT operator, Qpnqi , is weighted by the respective Wilson coefficients,cpnqi , over a power n-4 of a new physics scale, Λ, resulting in(1) LSM-EFT “ Lp4qSM `ÿi,ncpnqiΛn´4Qpnqi .Considering only the effect of dimension-six operators, it brings to a modification inthe total event yield, which results in the sum of an SM contribution, a linear interfer-ence term between the SM diagrams and a single operator, the pure BSM contribution,quadratically scaling with the Wilson coefficient, and the mixed interference term be-tween pairs of (same-dimension) operators.p˚q IFAE 2023 - “Energy Frontier” sessionp˚˚q Speaker on behalf of a collaboration between Torino (R. Bellan, A. Mecca, C. Tarriconeand A. Vagnerini) and Milano-Bicocca (G. Boldrini, F. Cetorelli, P. Govoni and A. Massironi)working groups.Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0) 12 C. TARRICONETable I. – Dependency of the studied processes on the bosonic EFT operators. Empty cellsindicate the absence of diagrams affected by a particular operator for that channel. The brack-ets indicate operators that introduce anomalies in the studied channels, but these effects arestrongly suppressed by the kinematic selection criteria. Hence, for the purpose of this study,these operators are neglected for the corresponding channels.QW QHB QHW QHWB QHD QHlWZγ X X X X XZZγ X X X XVZγ X X X X XQCD-Zγjj X XVZZ X (X) X X X (X)QCD-ZZjj X XThe triboson analyses traditionally neglect the dimension-six operators’ potential ef-fects focusing on the dimension-eight operators’ impact on quartic couplings. The talkwas based on ref. [1], that proved the potential impact of dimension-six operators ontriple and quartic gauge vertices, along with Higgs-mediated diagrams, is not negligi-ble for triboson production processes from 13 TeV proton-proton collisions at the LHC.In particular, the processes under study are the VZγ and VZZ production (V=W,Z).The W˘Zγ and ZZγ production processes are studied in the fully leptonic final statesgiven by μνμ e`e´ γ and μ`μ´ e`e´ γ, respectively. They are also studied in an inclusivesemi-leptonic channel, 2 jets` l`l´ γ, where the jets in the final state are the productof hadronizing quarks coming from the V boson decay. The VZZ production process isstudied in a semi-leptonic channel 2 jets` μ`μ´ e`e´. For the semi-leptonic channels,the processes with jet pairs induced by QCD vertices, denoted as QCD-ZZjj/QCD-Zγjj,are also included as backgrounds.The study focuses on the CP-even dimension-six bosonic operators of the Warsawbasis [2], excluding the ones inducing the gluon self-couplings and the anomalous cou-plings of gluons with the Higgs boson, namely QG and QHG, since they do not affectthe electroweak sector. The resulting set of operators considered in this work, inducingdiagrams for the processes of interest, is summarized in table I.2. – Generation and shape analysisThe event generation is performed at the leading order using the amplitude decomposi-tion technique with MadGraph5 aMC@NLO 2.6.5 [3] interfaced with the SMEFTsim3.0 package [4, 5]. Non-resonant diagrams are included (but kinematically suppressed),modeling all processes as full 2 Ñ 6 fermions and 2 Ñ 4 fermions + γ. The generationis also reproduced with the re-weighting technique to ensure the stability of the resultsin the profiled fit analysis for the semi-leptonic channels. A comprehensive descriptionof both the amplitude decomposition and re-weighting techniques is provided in ref. [6].Individual operator contributions and their interference are distinctly generated. TheSM term is generated with all BSM dynamics set to zero. In the context of the one-dimensional study (one operator at a time) only contributions of individual operatorsare considered. In the two-dimensional case, the interference contribution between pairsIMPACT OF DIMENSION-SIX EFT OPERATORS ON TRIBOSON PROCESSES AT THE LHC 3012345678EventsSM (EWK) SM Stat. Unc. Quad cWLin cW BSM cW=0.1 BSM cW=0.316BSM cW=1.0(13 TeV)-1300 fbSimulationγWZ1.2 1.4 1.6 1.8 2 2.2 2.4T0H02040BSM / SM012345678EventsSM (EWK) SM Stat. Unc. Quad cHDDLin cHDD BSM cHDD=0.316 BSM cHDD=1.0BSM cHDD=3.16(13 TeV)-1300 fbSimulationγZZ0 20 40 60 80 100 120 140 160 180 200[GeV]-μ-T,ep0123BSM / SMFig. 1. – The plot on the left shows the distribution obtained for the QW operator affectingthe WZγ production process as a function of the zero-th order Fox-Wolfram moment [8] HT0of the 3lνγ system, defined asřa,bPte˘,μ`,γpaT pbTppTot.Tq2, where pνT is the missing transverse energyper event. In this case, the shape of the EFT quadratic component is well resolved with respectto the SM one. The plot on the right shows the impact on the transverse momentum pe´μ´T ofthe same-sign charged leptons of the EFT components induced by the operator QHD affectingthe ZZγ production process. It is an example of non-negligible destructive interference of theQHD-induced diagrams with the SM component, that partially mitigated by the presence ofthe positive-definite quadratic component. Taken from Bellan R. et al., JHEP, 2023 (2023)158, https://doi.org/10.1007/JHEP08(2023)158, published under the terms of the CreativeCommons Attribution License https://creativecommons.org/licenses/by/4.0/.of operators is additionally considered. The interference terms between all the possibleoperator pairs in the specified subset are computed to derive the profiled constraints.The analysis is conducted under the assumption of CP symmetry conservation, U(3)5flavor symmetry, and {mW ,mZ , GF } as the input parameter scheme [7]. The eventselection applied is based on the phase space regions outlined in table 4 of ref. [1], wherethe variables studied are also listed channel by channel.Figure 1 shows two examples of distributions investigated. More examples of variablesexamined can be found in ref. [1]. The shape analysis allows the identification of a phase-space region where to isolate the potential EFT effects.3. – One-dimensional expected constraints on the Wilson coefficientsThe expected bounds on the Wilson coefficients associated with the operators underscrutiny are evaluated at the generator level for an integrated luminosity of 300 fb´1. Alikelihood scan is performed over the values of the Wilson coefficient ci in a fixed range,for each channel, from the distributions of all the variables of interest. This procedureis computed for each variable of interest using the Combine tool [9]. A comprehensivedescription of the likelihood scan construction is provided in ref. [1, 6]. From the likeli-hood scans, the 68%(95%) confidence level intervals in the ci estimates are extracted byrequiring ´2ΔlogL ă 1p3.84q [10], where L is the likelihood function. The confidenceintervals for the considered Wilson coefficients are evaluated neglecting theoretical andexperimental systematic uncertainties, with the exception of the luminosity uncertaintyof 2%, which affects the statistical precision of the results. The more stringent the es-timated constraints, the higher is the sensitivity to the kinematic anomalies inducedby the corresponding EFT operator. The global analysis of the sensitivity estimate is4 C. TARRICONETable II. – Confidence intervals on the estimates of the subset of Wilson coefficients con-sidered, extracted from the respective likelihood scan for the most sensitive variable, foreach channel studied. The last rows the confidence intervals obtained combining all thetriboson channels involving diagrams induced by operators individually included in the SMLagrangian, compared to the results coming from a VBS combination in the study ofref. [6] combining many VBS channels. The results are referred to a benchmark inte-grated luminosity of 300 fb´1. Taken from Bellan R. et al., JHEP, 2023 (2023) 158,https://doi.org/10.1007/JHEP08(2023)158, published under the terms of the Creative Com-mons Attribution License https://creativecommons.org/licenses/by/4.0/.Processes Op.s Ñ QW QHB QHW QHWB QHDBest var. pl1T pγT pZq pγT pZq pγT pZq pl1T pWZqWZγ 68% C.L. [-0.20,0.21] [-0.41,0.41] [-0.44,0.44] [-0.50,0.73] [-1.36,1.79]95% C.L. [-0.31,0.32] [-0.60,0.60] [-0.65,0.65] [-0.79,1.04] [-2.50,11.2]Best var. pγT pZ1q mμμ mμμ pe`μ`TZZγ 68% C.L. No [-0.62,0.61] [-0.68,0.68] [-0.81,1.06] [-1.91,4.55]95% C.L. diagrams [-0.90,0.90] [-0.98,0.99] [-1.23,1.49] [-3.27,6.53]Best var. pl1T mjj mjj pl1T pγq pl2T pγqVZγ 68% C.L. [-0.26,0.26] [-0.55,0.54] [-0.60,0.60] [-0.11,0.11] [-0.17,0.17]95% C.L. [-0.37,0.37] [-0.77,0.76] [-0.84,0.84] [-0.22,0.23] [-0.33,0.34]Best var. pl1T pVT mμμ pe`μ`TVZZ 68% C.L. [-0.63,0.63] Negligible [-4.78,4.08] [-0.80,0.65] [-2.73,1.82]95% C.L. [-0.97,0.97] [-6.91,6.17] [-2.22,1.20] [-3.78,2.82]VZZ/VZγ 68% C.L. [-0.18,0.19] [-0.37,0.37] [-0.40,0.40] [-0.11,0.11] [-0.17,0.17]comb. 95% C.L. [-0.27,0.28] [-0.53,0.53] [-0.57,0.57] [-0.21,0.21] [-0.33,0.33]VBS 95% C.L. [-0.19,0.18] - [-1.02,1.08] [-1.34,0.96] [-1.98,1.74]obtained by combining all the triboson production channels for the common operators.The best variable is identified by the sensitivity bounds at 68% confidence level. Ta-ble II summarizes the results of the one-dimensional scan. The sensitivity estimatesfor the semi-leptonic channels, VZZ and VZγ, include the effects of the QCD-inducedbackground processes.4. – Simultaneous constraints on different Wilson coefficientsThe analysis procedure is reproduced in the same way for the two-dimensional case,by inserting the operators pairwise into the fit. For each channel, the confidence regionsare extracted from the likelihood scans using the variable most sensitive to the operatorpair. The statistical combination of the likelihood is then performed for all the channels.IMPACT OF DIMENSION-SIX EFT OPERATORS ON TRIBOSON PROCESSES AT THE LHC 5(13 TeV)-1300 fbCombinedγZZγVZγWZVZZ4− 3− 2− 1− 0 1 2 3 4HWc1.5−1−0.5−00.511.52HBc(13 TeV)-1= 1 TeV, L = 300 fbΛ1− 0.5− 0 0.5 1Wc1−0.5−00.511.5HWc(13 TeV)-1= 1 TeV, L = 300 fbΛFig. 2. – Bi-dimensional likelihood contour levels at ´2Δ logL “ 2.3 from the triboson channelssensitive for the QHB-QHW and QW -QHW pairs of operators, respectively. In the case of thesemi-leptonic channels VZZ and VZγ, the QCD-induced backgrounds and the correspondingEFT contributions are included into the fit. The central plot shows the case of two operatorsinducing the same anomalous couplings between the Higgs boson and the neutral gauge bosons,for which a linear correlation between the estimates of the corresponding Wilson coefficientscan be observed. The latter is attributed to a large mutual interference term, since the linearinterference terms with the SM are negligible. The right plot illustrates a case for which thepotential anomalies induced by the QW operator in the considered processes can be regarded asuncorrelated with those caused by the other operators. Taken from Bellan R. et al., JHEP,2023 (2023) 158, https://doi.org/10.1007/JHEP08(2023)158, published under the terms ofthe Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/.Some examples of the corresponding 68% C.L. areas are shown in fig. 2. The completematrix of two-dimensional expected confidence regions associated with every possiblecouple of operators in the subset under study can be found in ref. [1].A global fit constraining the individual coefficients is also performed. Limits on asingle Wilson coefficient are derived by profiling all the other considered coefficients.Floating parameters are treated as unconstrained nuisances with a flat prior. The com-parison between the profiled and individual constraints at 95% C.L. for each Wilsoncoefficient is shown in fig. 3. An expected decrease in the sensitivity of the profiled fitwith respect to the individual constraints can be observed for the combination of all thetriboson channels under study. This effect is more pronounced for the EFT operatorsaffecting the couplings between Higgs and gauge bosons. This can be explained by thepresence of anomalies induced in the same vertices, leading to flat directions and largemutual interferences. The only exceptions are the anomalous effects induced by QW ,uncorrelated with the other operators, as observed in the two-dimensional contours infig. 2 for the tcW , cHW u case.5. – Summary and conclusionsThe first benchmark study of the sensitivity of triboson measurements to dimension-six SM-EFT operators was presented, addressing the study of the triboson fully leptonicWZγ and ZZγ channels, and the semi-leptonic inclusive VZγ and VZZ channels, whereV=W,Z. The study covers the main class of corrections affecting triple, quartic, andHiggs-gauge couplings, adopting a subset of the Warsaw basis CP-symmetric operatorswith tmW ,mZ , GF u as input parameters. EFT components for all channels and operatorswere generated at the parton level up to the Λ´4 order. The sensitivity constraints arecomputed for a LHC measurement with proton-proton collisions at a center-of-massenergy of 13 TeV and for a projected total luminosity of 300 fb´1.The study reveals that the semi-leptonic VZγ channel is the most sensitive to bosonicoperators. The leading lepton transverse momentum imposes strong constraints onanomalous triple and quartic gauge boson couplings, showcasing competitive sensitiv-6 C. TARRICONE0 2 4 6 88− 6− 4− 2−[-0.31 , 0.31]Wc [-0.27 , 0.28][-1.18 , 1.20]HBc [-0.53 , 0.53][-2.21 , 2.47]HWBc [-0.21 , 0.21][-2.29 , 2.85]HWc [-0.57 , 0.57][-4.39 , 6.27]HDc [-0.33 , 0.33]ProfiledCombination-1= 1 TeV, L = 300 fbΛ95% C.L., 13 TeV, Parameter estimateProfiledIndividualProfiled IndividualSMFig. 3. – Comparison between the profiled and the individual expected constraints (quadraticscale) on the Wilson coefficients from the combination of the leptonic channels WZγ,ZZγ, and the semi-leptonic channels VZγ, VZZ. The solid dots denote the SM expec-tation. Gray-filled boxes indicate the 95% C.L. intervals obtained by estimating thecorresponding Wilson coefficient as the parameter of interest, with all the other coeffi-cients left floating in the maximum interval (-20,20). Green-filled boxes indicate the 95%C.L. individual constraints. Taken from Bellan R. et al., JHEP, 2023 (2023) 158,https://doi.org/10.1007/JHEP08(2023)158, published under the terms of the Creative Com-mons Attribution License https://creativecommons.org/licenses/by/4.0/.ity with existing literature on vector boson scattering analyses.Results from the two-dimensional scan of operators illustrate complementarity and in-terplay between different measurements, highlighting orthogonal directions in sensitivityfor different pairs of operators. The study also explores the impact of mutual interfer-ence terms in the fit, revealing linear (anti-)correlation in sensitivity to pairs of operators.Constraints on the individual Wilson coefficients are also extracted by profiling all theother coefficients in the set of interest. A non-negligible decrease of is highlighted by theprofiled fit, but it does not compromise the constraining power of these analyses to theanomalies induced by dimension-six operators.Possible improvements of the study presented include the refinement of this analysisto account for detector reconstruction effects and a more detailed treatment of reduciblebackground processes. The scope of the investigation can be further expanded in thefuture through the development of new models considering the next terms in the am-plitude of the scattering matrix, namely the linear interference term of dimension-eightoperators with the SM diagrams, and the mixed interference between dimension-six anddimension-eight operators.REFERENCES[1] Bellan R. et al., J. High Energy Phys., 08 (2023) 158.[2] Grzadkowski B. et al., J. High Energy Phys., 10 (2010) 085.[3] Alwall J. et al., J. High Energy Phys., 07 (2014) 079.[4] Brivio I. et al., J. High Energy Phys., 12 (2017) 070.[5] Brivio I., J. High Energy Phys., 04 (2021) 073.[6] Bellan R. et al., J. High Energy Phys., 05 (2022) 039.[7] Brivio I. et al., CERN-LPCC-2021-002, 11 (2021).[8] Fox G. C. and Wolfram S., Nucl. Phys. B, 149 (1979) 413.[9] The CMS Collaboration, Eur. Phys. J. C, 75 (2015) 212.[10] The Particle Data Group Collaboration, Prog. Theor. Exp. Phys., 8 (2020) 083C01.

Impact of dimension-six EFT operators on triboson processes at the LHC

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Impact of dimension-six EFT operators on triboson processes at the LHC

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