Research Article  Open Access
Constraints on Higgs Effective Couplings in Production of CLIC at 380 GeV
Abstract
The potential of the process in the first stage of CLIC considering centerofmass energy of 380 GeV and assuming the baseline integrated luminosity of 500 is examined to probe CPconserving dimensionsix operators in a modelindependent Standard Model effective field theory framework. In the analysis, a detailed fast simulation on signal processes and dominant backgrounds is performed including parton showering with PYTHIA and detector simulation based on ILD type detector with DELPHES in MadGraph. The obtained best limits on , , and are , , and , respectively.
1. Introduction
The recent Large Hadron Collider (LHC) discovery of a scalar particle with 125 GeV which is compatible with Standard Model (SM) Higgs boson predicted by BroutEnglertHiggs symmetry breaking mechanism opens up a gateway to search for physics beyond the SM [1, 2]. But evidence for new physics beyond the SM using analysis of combined ATLAS and CMS data for probing the couplings of Higgs boson has not been observed yet. Possible deviation from the SM predictions of Higgs boson couplings would imply the presence of new physics involving massive particles that are decoupled at energy scales much larger than the Higgs sector energies being probed [3]. The SM Effective Field Theory (EFT) is a wellknown modelindependent method for investigation of any deviation from SM [4, 5]. The origin of this method is based on all new physics contributions to the SM described by a systematic expansion in a series of high dimensional operators beyond the SM fields. All high dimensional operators conform to SM gauge symmetry. The dimension6 operators play an important role in the framework since they match ultraviolet (UV) models which are simplified by the universal oneloop effective action. There have been many analyses for constraints on SM EFT operators with available data from LHCRun 1 [6–13] and with electroweak precision measurements provided from a previous accelerator, namely, Large Electron Positron (LEP) [14–17]. In particular, the prediction on dimension6 operators has been examined in many rewarding studies at High Luminosity LHC (HLLHC) [18–20] and future colliders [21–29].
The precision measurements of Higgs boson couplings with the other SM particles at the LHC and planned future colliders will give us detailed information about its true nature. The future multiTeV colliders with extremely high luminosity and clean environment due to the absence of hadronic initial state would grant access to precise measurement, especially for the Higgs couplings. The Compact Linear Collider (CLIC) is one of the mature proposed linear colliders with centerofmass energies from a few hundred GeV up to 3 TeV [30]. The first energy stage of CLIC operation was chosen to be = 380 GeV, with the predicted integrated luminosity of 500 . The primary motivation of this stage is the precision measurements of SM Higgs properties and also the modelindependent Higgs couplings to both fermions and bosons [30, 31].
In this study, we focus on the analysis of production process in order to assess the projection of the first energy stage of the CLIC on the CPconserving dimension6 operators involving the Higgs and gauge bosons (, , ) defined by an SM EFT Lagrangian in the next section.
2. Effective Operators
The wellknown SM Lagrangian () involving renormalizable interactions is suppressed by higher dimensional operators in SM EFT approach. All these operators are parametrized by an energy scale of nonobserved states assumed larger than vacuum expectation value of Higgs field (). A few different operator bases are presented in the literature; we consider SM EFT operators as the strongly interacting light Higgs Lagrangian () in bar convention [18, 33, 34]. Assuming the baryon and lepton number conservation, the most general form of dimension6 effective Lagrangian including Higgs boson couplings that keep SM gauge symmetry is given as follows:where are normalized Wilson coefficients that are free parameters. In this work, we consider the dimension6 CPconserving interactions of the Higgs boson and electroweak gauge boson in SILH basis as [34]where represents the Higgs quartic coupling; , , and are the Yukawa coupling matrices in flavor space; , , and denote coupling constant of , , and gauge fields, respectively; the generators of in the fundamental representation are given by , being the Pauli matrices; is Higgs field that contains a single doublet of fields; and are the electroweak field strength tensors; is the strong field strength tensors; and the Hermitian derivative operators are defined as . The SM EFT Lagrangian (see (2)) containing the Wilson coefficients in the SILH bases of dimension6 CPconserving operators can be defined in terms of the mass eigenstates after electroweak symmetry breaking (Higgs boson, , , photon, etc.) as follows:where , , and are the field strength tensors of boson, boson, and photon, respectively; represents the mass of the Higgs boson; the effective couplings in gauge basis defined as dimension6 operators are given in Table 1 in which () coupling is the SM contribution to the Higgs boson to two photons’ (gluons) vertex at loop level.
We use the parametrization in [34] based on the formulation given in [33] in our analysis. The parametrization is not complete as described in detail in Section 3 of [35] and also [36]. It chooses to remove two fermionic invariants while retaining all the bosonic operators. This choice assumes completely unbroken flavor symmetry of the UV theory where the coefficients of these operators are unit matrices in flavor space. Therefore, we assume flavor diagonal dimensionsix effects. It is sufficient for the purpose of this paper in which we do not consider higher order electroweak effects but only claim a sensitivity study for , , , , and couplings.
We have used the Monte Carlo simulations with leading order in MadGraph5_aMC@NLO [37] involving effect of the dimension6 operators on production mechanism in collisions. The effective Lagrangian of the SM EFT in (2) is implemented into the MadGraph5_aMC@NLO based on FeynRules [38] and UFO [39] framework. In this study, we focus on searching for the dimension6 Higgsgauge boson couplings via process as shown in Figure 1. This process is sensitive to Higgsgauge boson couplings; , , and and the couplings of a quark or lepton pair and one single Higgs field; and , , and in the mass basis. In the gauge basis, process is sensitive to the seven Wilson coefficients—, , , , , , and —related to Higgsgauge boson couplings and also effective fermionic couplings. Due to the small Yukawa couplings of the first and secondgeneration fermions, we neglect the effective fermionic couplings. We set and to zero in all our calculations since the linear combination of and is strongly constrained from the electroweak precision test of the oblique parameters and . The cross sections of process as a function of , , , , and couplings are shown in Figure 2. There have been many studies in the literature considering individual, subset, or simultaneous change of dimension6 operators [23, 26]. Here, we vary individually dimension6 operators and calculate the contributions to the corrections from new physics in the analysis. We presume that only one of the effective couplings is nonzero at any given time, while the other couplings are fixed to zero. One can easily see the deviation from SM for these couplings even in a small value region for process. Therefore, we will only consider these five among the Higgsgauge boson effective couplings in the detailed analysis including detector simulations through the process at CLIC with 380 GeV centerofmass energy in the next section.
3. Signal and Background Analysis
We perform the detailed analysis of , , , , and effective couplings via process as well as other relevant backgrounds at the first energy stage of CLIC. The signal process includes both schannel process (Higgsstrahlung) and tchannel process (WWfusion) as shown in Figure 1. In the initial energy stage of CLIC at = 380 GeV, these two processes have approximately the same amount of contribution to the production cross section of the process. In our analysis, we include effective dimension6 couplings and SM contribution as well as interference between effective couplings and SM contributions () that lead to process where Higgs decays to a pair of quarks. We consider the following relevant backgrounds: : process which has the same final state of the considered signal process including only SM contribution where the Higgs decays to a pair of quarks; : process where one decays to and the other decays to ; : process where two quarks are from decaying to in which decay leptonically; : process in which decays to . The generated signal and all backgrounds at parton level in MadGraph5_aMC@NLO are passed through Pythia 6 [40] for parton shower and hadronization. The detector responses are taken into account with ILD detector card [41] in Delphes 3.3.3 [42] package. Then, all events are analyzed using the ExRootAnalysis utility [43] with ROOT [44].
Requiring missing energy transverse (), no charged leptons and at least 2 jets with their transverse momenta () greater than 20 GeV and pseudorapidity () between −2.5 and 2.5 are the preselection of the event to be further analyzed. The energy resolution of jets for is assumed to beThe momentum resolution for jets as a function of and isJets are clustered with the anti algorithm [45] using FastJet [46] where a cone radius is used as . In order to select the signal and background events, the following kinematic cuts and requirements are applied. (i) At least two jets tagged as the jet are required, which significantly suppresses the lightquark jet backgrounds; these two jets are used to reconstruct Higgs bosonmass. (ii) One of the tagged jets with the highest is defined as while the other is with lower . Figure 3 shows distributions of and of signal (for = 0.05) and all relevant background processes versus reconstructed Higgs bosonmass from and (). As it can be seen in Figure 3, with GeV, with GeV, and pseudorapidity of the tagged jets to be are considered to reduce and . In ILD detector card, both tagging efficiency and misidentification rates are given as a function of jet transverse momentum. For the transverse momentum of leading jet () ranging from 50 GeV to 180 GeV, tagging efficiency is between 64% and 72%, jet misidentification rate is 17%–20%, and misidentification rate of light jet is 1.2%–1.76%. The missing transverse energy () and scalar transverse energy sum () for signal (for = 0.05) and all relevant background processes versus are shown in Figure 4. (iii) The missing transverse energy is required to be GeV to suppress the backgrounds at low missing energy region. (iv) In particular, to reduce background process, the scalar transverse energy sum () is required to be 100 GeV 200 GeV. Normalized distributions of reconstructed invariant mass of Higgs boson from for signal with , , , and and relevant background processes are given in Figure 5. (v) Finally, the reconstructed invariant mass of Higgs boson from two jets is selected to be in the range 92 GeV < < 136 GeV. The kinematic distributions for each process are normalized to the number of expected events which is defined to be the cross section of each process time integrated luminosity with = 500 fb^{−1}.
(a)
(b)
(a)
(b)
Effects of the cuts used in the analysis can be seen from Table 2, which shows the number of events after each cut. Requiring two tagged jets reduces the , , and backgrounds more than signal and background with the same final state, . Cut2 affects both signal and all relevant backgrounds, especially and . cut decreases both and backgrounds while cut significantly suppresses background. Final effect of all cuts is approximately 15% for signal and background and 0.3%–0.8% for other relevant backgrounds.

4. Sensitivity of HiggsGauge Boson Couplings
We calculate the sensitivity of the dimension6 Higgsgauge boson couplings in process by applying criterion with and without a systematic error. The function is defined as follows:where is the total number of events in the existence of effective couplings () and total backgrounds (, , , and ), is the number of events of total backgrounds in th bin of the invariant mass distributions of reconstructed Higgs boson, and is the combined systematic () and statistical errors in each bin. So, the numerator in (6) is equal to the number of extra events due to the presence of new operators. In this analysis, we focused on , , and couplings which are the main coefficients contributing to signal process. The 95% Confidence Level (CL) limits including only statistical error on dimension6 Higgsgauge boson couplings at = 380 GeV and = 500 fb^{−1} (CLIC380) are compared with the LHC at 14 TeV centerofmass energies for the integrated luminosity of 300 fb^{−1} (LHC300) and 3000 fb^{−1} (LHC3000) [18] in Figure 6. We see that CLIC380 results would be significantly more sensitive to and somewhat sensitive to , whereas sensitivity to is comparable with expected LHC results. The prediction on the limits for the future lepton colliders: ILC [23, 28] of an integrated luminosity = 300 fb^{−1} at the centerofmass energy = 500 GeV, FCCee [23] for = 10 at 240 GeV, and CEPC [32] for = 5 at = 240 GeV are also shown in Figure 6. In order to include the systematical uncertainties, we recompute the bounds. For example, including a 10% conservative systematic uncertainty, the constraint on is . This bound is four times lower than the obtained limits without systematic uncertainties.
5. Conclusions
We have investigated the CPconserving dimension6 operators of Higgs boson with other SM gauge bosons via process using an effective Lagrangian approach at first energy stage of CLIC ( GeV, = 500 fb^{−1}). We have used leadingorder strongly interacting light Higgs basis assuming vanishing treelevel electroweak oblique parameterization and flavor universality of the new physics sector. We analyzed only hadronic () decay channel of the Higgs boson including dominant background processes by considering realistic detector effect in the analysis. We have shown the kinematic distributions of jets in final state, missing transverse energy, scalar transverse energy sum, and invariant mass distributions. Due to the fact that the signal final state consists of two neutrinos and two jets, the distributions of missing transverse energy and scalar transverse energy sum are performed for determining a cutbased analysis. We have obtained 95% CL limits on dimensionsix operators analyzing invariant mass distributions of two jets from Higgs decay in signal process and the other dominant backgrounds. The process is more sensitive to couplings than the other dimensionsix couplings at first energy stage of CLIC. Our results show that a CLIC with GeV and = 500 fb^{−1} will be able to probe the dimensionsix couplings of Higgsgauge boson interactions in process especially for couplings at scales beyond the HLLHC bounds while they become competitive with the , couplings.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was partially supported by the Abant Izzet Baysal University Scientific Research Projects under Project no. 2017.03.02.1137. H. Denizli’s work was partially supported by the Turkish Atomic Energy Authority (TAEK) under Grant no. 2013TAEKCERNA5.H2.P1.0124. The authors would like to thank the CLICdp group for the discussions, especially Philipp G. Roloff for valuable suggestions in the CLICdp Working Group analysis meeting. The authors would also like to thank L. Linssen for encouraging them to get involved in CLICdp collaboration.
References
 ATLAS Collaboration, G. Aad, T. Abajyan et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Physics Letters B, vol. 716, no. 1, pp. 1–29, 2012. View at: Google Scholar
 CMS Collaboration, S. Chatrchyan, V. Khachatryan et al., “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Physics Letters B, vol. 716, no. 1, pp. 30–61, 2012. View at: Google Scholar
 T. Appelquist and J. Carazzone, “Infrared singularities and massive fields,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 11, no. 10, pp. 2856–2861, 1975. View at: Publisher Site  Google Scholar
 W. Buchmuller and D. Wyler, “Effective lagrangian analysis of new interactions and flavour conservation,” Nuclear Physics B, vol. 268, pp. 621–653, 1986. View at: Publisher Site  Google Scholar
 B. Grzadkowski, M. Iskrzyński, M. Misiak, and J. Rosiek, “Dimensionsix terms in the Standard Model Lagrangian,” Journal of High Energy Physics, vol. 85, no. 10, 2010. View at: Publisher Site  Google Scholar
 T. Corbett, O. J. Éboli, J. GonzalezFraile, and M. C. GonzalezGarcia, “Robust determination of the Higgs couplings: Power to the data,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 87, no. 1, 2013. View at: Publisher Site  Google Scholar
 J. Ellis, V. Sanz, and T. You, “The Effective Standard Model after LHC Run I,” High Energy Physics, vol. 157, https://arxiv.org/abs/1410.7703. View at: Google Scholar
 J. Ellis, V. Sanz, and T. You, “Complete Higgs Sector Constraints on Dimension6 Operators,” Journal of High Energy Physics, vol. 36, 2014. View at: Google Scholar
 A. Falkowski, “Effective field theory approach to LHC Higgs data,” Pramana, vol. 3, article 39, 2016. View at: Google Scholar
 T. Corbett, O. J. Éboli, D. Gonçalves, J. GonzalezFraile, T. Plehn, and M. Rauch, “The Higgs legacy of the LHC Run I,” Journal of High Energy Physics, vol. 156, https://arxiv.org/abs/1505.05516. View at: Google Scholar
 F. Ferreira, B. Fuks, V. Sanz, and D. Sengupta, “High Energy Physics  PhenomenologyProbing CPviolating Higgs and gauge boson couplings in the Standard Model effective field theory,” The European Physical Journal C, vol. 77, no. 675, 2017. View at: Google Scholar
 ATLAS Collaboration, G. Aad, B. Abbott et al., “Constraints on nonStandard Model Higgs boson interactions in an effective Lagrangian using differential cross sections measured in the H→γγ decay channel at √s=8 TeV with the ATLAS detector,” Physics Letters B, vol. 753, no. 69, pp. 69–85, 2016. View at: Google Scholar
 D. R. Green, P. Meade, and M. A. Pleier, “MultiBoson Interactions at the LHC,” Reviews of Modern Physics, vol. 89, article 035008, 2017. View at: Google Scholar
 D. Jones and S. Petcov, “Heavy Higgs bosons at LEP,” Physics Letters B, vol. 84, no. 4, pp. 440–444, 1979. View at: Publisher Site  Google Scholar
 B. Grinstein and M. B. Wise, “Operator analysis for precision electroweak physics,” Physics Letters B, vol. 265, no. 34, pp. 326–334, 1991. View at: Publisher Site  Google Scholar
 K. Hagiwara, R. Szalapski, and D. Zeppenfeld, “Anomalous Higgs boson production and decay,” Physics Letters B, vol. 318, no. 1, pp. 155–162, 1993. View at: Publisher Site  Google Scholar
 Z. Han and W. Skiba, “Effective theory analysis of precision electroweak data,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 71, p. 075009, 2005. View at: Publisher Site  Google Scholar
 C. Englert, R. Kogler, H. Schulz, and M. Spannowsky, “Higgs coupling measurements at the LHC,” The European Physical Journal C, vol. 76, no. 7, 2016. View at: Publisher Site  Google Scholar
 A. Buckley, C. Englert, J. Ferrando et al., “Constraining top quark effective theory in the LHC Run II era,” Journal of High Energy Physics, vol. 1604, no. 015, 2016. View at: Google Scholar
 H. Khanpour, S. Khatibi, and M. Mohammadi Najafabadi, “Probing Higgs boson couplings in H + γ production at the LHC,” Physics Letters B, vol. 773, pp. 462–469, 2017. View at: Publisher Site  Google Scholar
 G. Amar, S. Banerjee, S. von Buddenbrock et al., “Exploration of the tensor structure of the Higgs boson coupling to weak bosons in e + e − collisions,” Journal of High Energy Physics, vol. 2015, no. 2, 2015. View at: Publisher Site  Google Scholar
 S. Kumar, P. Poulose, and S. Sahoo, “Study of Higgsgauge boson anomalous couplings through,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 91, no. 7, 2015. View at: Publisher Site  Google Scholar
 J. Ellis and T. You, “Sensitivities of Prospective Future e+e Colliders to Decoupled New Physics,” Journal of High Energy Physics, vol. 1603, no. 089, 2016. View at: Google Scholar
 S. F. Ge, H. J. He, and R. Q. Xiao, “Probing New Physics Scales from Higgs and Electroweak Observables at e^{+}e^{−} Higgs Factory,” Journal of High Energy Physics, vol. 1610, no. 007, 2016. View at: Google Scholar
 J. Cohen, S. BarShalom, and G. Eilam, “Contact interactions in Higgsvector boson associated production at the ILC,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 94, no. 3, 2016. View at: Publisher Site  Google Scholar
 J. Ellis, P. Roloff, V. Sanz, and T. You, “Dimension6 operator analysis of the CLIC sensitivity to new physics,” Journal of High Energy Physics, vol. 2017, no. 5, 2017. View at: Publisher Site  Google Scholar
 S. Alam, S. Behera, S. Kumar, and S. Sahoo, “Constraining capability of Zγh production at the ILC,” International Journal of Modern Physics A, vol. 32, no. 02n03, 2017. View at: Google Scholar
 H. Khanpour and M. M. Najafabadi, “Constraining Higgs boson effective couplings at electronpositron colliders,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 95, no. 5, 2017. View at: Publisher Site  Google Scholar
 C. Englert, Q. Li, M. Spannowsky, M. Wang, and L. Wang, “VBS W^{±}W^{±}H production at the HLLHC and a 100 TeV ppcollider,” High Energy Physics  Phenomenology, vol. 32, no. 18, https://arxiv.org/abs/1702.01930. View at: Google Scholar
 CLIC and CLICdp Collaborations, M. J. Boland, U. Felzmann, P. J. Giansiracusa et al., “Updated baseline for a staged Compact Linear Collider,” CERN Yellow Reports, vol. 4, 2016. View at: Publisher Site  Google Scholar
 H. Abramowicz, A. Abusleme, K. Afanaciev et al., “Higgs Physics at the CLIC ElectronPositron Linear Collider,” The European Physical Journal C, vol. 77, no. 475, 2017. View at: Google Scholar
 S. F. Ge, H. J. He, and R. Q. Xiao, “Testing Higgs Coupling Precision and New Physics Scales at Lepton Colliders,” International Journal of Modern Physics A, vol. 31, no. 33, article 1644004, 2016. View at: Google Scholar
 R. Contino, M. Ghezzi, C. Grojean, M. Mühlleitner, and M. Spira, “Effective Lagrangian for a light Higgslike scalar,” Journal of High Energy Physics, vol. 2013, no. 7, 2013. View at: Publisher Site  Google Scholar
 A. Alloul, B. Fuks, and V. Sanz, “Phenomenology of the Higgs Effective Lagrangian via FeynRules,” Journal of High Energy Physics, vol. 110, 2014. View at: Google Scholar
 R. Alonso, E. E. Jenkins, A. V. Manohar, and M. Trott, “Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology,” Journal of High Energy Physics, vol. 159, 2014. View at: Google Scholar
 I. Brivio and M. Trott, “Scheming in the SMEFT... and a reparameterization invariance!,” Journal of High Energy Physics, vol. 148, 2017. View at: Google Scholar
 J. Alwall, R. Frederix, S. Frixione et al., “The automated computation of treelevel and nexttoleading order differential cross sections, and their matching to parton shower simulations,” Journal of High Energy Physics, vol. 79, 2014. View at: Google Scholar
 A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, “FeynRules 2.0  A complete toolbox for treelevel phenomenology,” Computer Physics Communications, vol. 185, no. 8, pp. 2250–2300, 2014. View at: Publisher Site  Google Scholar
 C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer, and T. Reiter, “UFO—the universal FeynRules output,” Computer Physics Communications, vol. 183, no. 6, pp. 1201–1214, 2012. View at: Publisher Site  Google Scholar
 T. Sjöstrand, S. Mrenna, and P. Skands, “PYTHIA 6.4 physics and manual,” Journal of High Energy Physics, vol. 5, article 026, 2006. View at: Publisher Site  Google Scholar
 T. Behnke, J. E. Brau, and P. N. Burrows, The International Linear Collider Technical Design Report  Volume 4: Detectors, https://arxiv.org/abs/1306.6329.
 J. de Favereau, C. Delaere, P. Demin et al., “DELPHES 3, A modular framework for fast simulation of a generic collider experiment,” Journal of High Energy Physics, vol. 1402, no. 057, 2014. View at: Google Scholar
 http://madgraph.hep.uiuc.edu/Downloads/ExRootAnalysis.
 R. Brun and F. Rademakers, “ROOT: An object oriented data analysis framework,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 389, no. 81, 1997. View at: Publisher Site  Google Scholar
 M. Cacciari, G. P. Salam, and G. Soyez, “The Antik(t) jet clustering algorithm,” Journal of High Energy Physics, vol. 2008, article 063, 2008. View at: Publisher Site  Google Scholar
 M. Cacciari, G. P. Salam, and G. Soyez, “FastJet user manual: (For version 3.0.2),” The European Physical Journal C, vol. 72, no. 3, article 1896, pp. 1–54, 2012. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2018 H. Denizli and A. Senol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.