Search for the limits on anomalous neutral triple gauge couplings via $ZZ$ production in the $\ell \ell \nu \nu$ channel at FCC-hh

This paper presents the projections on the anomalous neutral triple gauge couplings ($aNTGC$) via $pp \rightarrow ZZ$ production in the 2$\ell$2$\nu$ final state at a 100 TeV proton-proton collider, \verb"FCC-hh". %100 TeV center of mass energy of The realistic \verb"FCC-hh"detector environments and its effects taken into account in the analysis. The study is carried out in the mode where one Z boson decays into a pair of same-flavor, opposite-sign leptons (electrons or muons) and the other one decays to the two neutrinos. The new bounds on the charge-parity (CP)-conserving couplings $C_{\widetilde{B}W} / \Lambda^{4}$ and CP-violating couplings $C_{WW} / \Lambda^{4}$, $C_{BW} / \Lambda^{4}$ and $C_{BB} / \Lambda^{4}$ achived at 95\% Confidence Level (C.L.) using the transverse momentum of the dilepton system ($p_{T}^{\ell \ell}$) are $[-\, 0.042, \,\, +\,0.042]$, $[-\,0.050, \,\, +\,0.050]$, $[-\,0.050, \,\, +\,0.050]$, and $[-\,0.048, \,\, +\,0.048]$ in units of TeV$^{-4}$, respectively.


I. INTRODUCTION
Production of gauge boson pairs has an important role in the tests of the non-Abelian SU (2) L × U (1) Y gauge group of the electroweak sector of the Standard Model (SM) and exploring the new physics at the TeV scale. Additionaly, diboson production is also connected to the spontaneous breaking of the EW gauge symmetry [1,2]. For this reason, a signature of new physics beyond SM may reveal themselves via the possible deviation from SM expected values in neutral triple tuning (NTG) couplings (which includes ZZγ, Zγγ and ZZZ vertices).
New physics effects at high energy physics can be described in the terms of the Effective Field Theory (EFT) parameters. This parameters is comprehensive to indicate the most likely places to observe these effects; besides they cover the gauge symmetries of the SM and can be used at both tree level and loop level. In the framework of EFT theory, one can include the Anomalous NTG vertices in an effective Lagrangian and it can be described by CP-conserving and CP-violating couplings, even though there is no electroweak NTGC exists at the tree level [3,4].
The dimension-eight (dim-8) effective Lagrangian for nTGC in the EFT framework taking into account the local U(1) EM and Lorentz symmetry can be given as [5] where i is defined as an index of equations working over the operators written as where B µν is the dual B strength tensor. The layout given in the formula of the operators with σ I σ J = δ I J /2 and It is expected that the main contribution of new physics to the amplitude of f f → ZZ process is com- * aliyilmaz@giresun.edu.tr ing from the interference between the SM and the dim-8 operators when the new physics energy scale is high. The square of the amplitude with dim-8 operators does not carry a significant contribution from the heavy new physics except that the interferences between the SM and the dim-8 and dimension-ten (dim-10) operators are excessively suppressed.
The dim-6 operators can influence on nTGC at one-arXiv:2102.01989v1 [hep-ph] 3 Feb 2021 loop level (at the order O(αŝ/4πΛ 2 ) despite being not effective at the tree level [5]. Nevertheless, the tree level contributions from dim-8 operators are of the order O(ŝv 2 /Λ 4 ). For this reason, a one-loop contribution of the dim-6 operators can be neglected in accordance with dim-8 operators considering Λ < ∼ 2v π/α. The coefficients of four dim-8 operators describing in Eq. 2 are the CP-conserving couplings C BW /Λ 4 and CPviolating couplings C W W /Λ 4 , C BW /Λ 4 and C BB /Λ 4 . These are couplings of the dim-8 operators transformed from the aTGC given in the Ref. [5] The νν final state via the production of ZZ dibosons has been carried out at Fermilab (CDF) collaboration [6,7] and DØ collaborations [8]. Recently, the ATLAS [9] ( at √ s = 13 TeV, corresponding to an integrated luminosity of 36.1 fb −1 ) and CMS [10] experiments also reported the bounds on the EFT parameters using the νν final state. This high energy results in an improvement of the cross section, that expands the scope of triple gauge coupling studies.
Additionally numerous phenomenological studies have been carried out the investigating the limits of aNTGCs at hadron colliders in the EFT framework [11][12][13][14][15][16][17]. Ta  For the future collider project, there are proposals for the future higher energy hadron colliders to carry out the researches directly at the energy frontier. These proposals include FCC-ee, FCC-eh and FCC-hh collider types working at different center of mass energies. The hadron collider option of FCC (FCC-hh) is planned to run at the center of mass energy of 100 TeV and the integrated luminosity of 1 ab −1 (initial) and 30 ab −1 (ultimate) [20,21].
Searching the new physics effects in the production of a diboson is requiring great effort. In the literature ZZ diboson production has been examined in two decay channels, such as the "4 " and " νν" channel [4]. In the ZZ → 4 decay channel, both of the Z bosons decay into two same-flavor, oppositely charged leptons. This process gives rise to the inclusion of a very low background, being kinematically reconstructable in the final state. In the ZZ → νν channel, one of the Z decays into a same-flavor, oppositely-charged two leptons, while the other one decays into neutrinos, which leads to an increase in the missing transverse energy in the final state. The branching ratio of " νν" final state is greater than the "4 " final state and the sensitivity to anomalous triple gauge couplings (aTGCs) would be higher than the "4 " final state. " νν" final state is still exposed to a larger background contamination, and it requires strict experimental selection which leads to force one Z boson boosted against the other in the transverse plane is necessary to retain the background at a more feasible level [22]. Hence, the " νν" final state includes more data quantities than the "4 " final state for the events with high-p T Z bosons, and this final state also presents competitive precision for integrated and differential measurements, as well as good sensitivity to aTGCs [23]. Therefore, the νν final state is chosen to analyze using the FCChh option could be open a new possibility to extent the most stringent upper limits on EFT parameters thanks to its high center-of mass energy 100 TeV and capability to reach L int = 30 ab −1 (ultimately).
This paper is arranged as follows: In Sect. II provides details of the simulation environment for the ZZ diboson signal and background production samples at the FCChh collider. Sect. III describes the algorithms developed for event selection strategies of this phenomenological study in the νν final state. Obtained results for the νν final state analysis are given in Sect. IV. Finally, conclusions on the main results and findings of each couplings are given in Sect. V.

II. GENERATION OF SIGNAL AND BACKGROUND EVENTS
In this section, we present the production of the pp → ZZ → + − νν signal events as well as the background events (SM) taking into account the experimental conditions of FCC-hh. In order to find the bounds on the aNTG couplings, we used the UFO model file [24] implemented into Monte Carlo (MC) event generator MadGraph5_aMC@NLO v2.6.4 [25]. The PYTHIA v8.2 [26] package is utilized for the parton showering, fragmentation and hadronization of generated signal and background events. The LHAPDF v6.1.6 [27] library with NNPDF v2.3 [28,29] set is a default set of parton distribution functions (PDFs) used to produce all MC samples. The jets were collected by using FastJet [30] where the anti-k T algorithm [31] already implemented with a cone radius is R = 0.4. In the search of new physics effects, 3 × 10 6 events are generated for the signal process, pp → ZZ, as well as the background process (in the same final state with signal process) by varying one coupling value at a time on each of the dim-8 cou-plings. The realistic detector effects are taken into account by using the FCC-hh detector card presents inside the Delphes v3.4.1 [32]. All generated events are analyzed by using the ExRootAnalysis [33] package with ROOT v6.16 [34]. The expected event numbers given in the plots of kinematic variables are weighted with the cross-section of each process including the branching times integrated luminosity of L int = 10 ab −1 . Since Feynman diagrams may simplify and vizualize the aNTGC vertices clearly, the leading order Feynman diagrams contibuting to the signal and background processes are depicted in Fig. 1(a) and Fig. 1(b), respectively. The blue dot indicates the aNTGC vertex in the ZZ process where one of Z decays into and the other one decays into νν final states. The deviation from the SM value shows that the main contribution for the signal is seen in the CP-conserving coupling (see Fig. 2). So the effective dim-8 aNTG operators and a SM contribution as well as interference between effective operators and SM contributions are considered in the analysis.

III. EVENT SELECTION
This analysis considers the pp → ZZ in the νν final state based on Ref. [23]. The candidate event selection procedure against larger background is optimized to handle with the contaminations. In this topology the two Z bosons originating from the aNTGC desired to be in opposite direction (back-to-back).
The pre-selection requirement in the analysis is the existence of one dilepton of the same flavor with opposite charge to construct the Z-boson. The missing transverse momentum E miss T is computed as a negative vector sum of all charged leptons and jets in the event. The events are required to have at least 2 leptons (N ≥ 2) of the same flavor with opposite charge (e + e − or µ + µ − ). Transverse momentum of leading lepton 1 , (subleading lepton 2 ), p T > 30 (20) GeV is required and the cut on the pseudo-rapidity between two leptons is also applied as |η | < 2.5. Events with relatively a few calorimeter activity are rejected by vetoing on the presence of more than one jet with p T > 20 and |η j | < 4.5 in the detector. The events selection is optimized by imposing the transverse momentum balance ratio (p miss The distance ∆R between two objects in η-φ plane is evaluated by the function ∆R = ∆η 2 + ∆φ 2 and we accepted the leptons only if the distance between lepton and jet, ∆R j is greater than 0.4 for further reducing the contributions of overlapping jet. In addition to previous cuts requiring the events having any extra lepton with p T > 10 GeV. Suppressing the effect of jet energy scale uncertainties, we applied extra cuts on the jets which are selected to have p T > 35 GeV for the central region|η| < 2.4 and p T > 40 GeV for the forward region 2.4 < |η| < 4.5. The dilepton invariant mass.(m ) is required to be within 15 GeV of the nominal Z boson mass. Candidate events are required to have E miss T > 110 GeV, and the distance ∆R between two leptons in η-φ plane is required to be greater than 2.1 which imposes the leptons must be close to each other. Only if the azimuthal angle difference between the missing transverse momentum E miss T and the dilepton system, ∆φ( E miss T , p T ) > 2.5 radian is accepted. Finally, the candidate events constructed from p is used for further analysis.
The kinematical distributions used to probe the signal from background in this analysis are plotted in Fig. 3 and Fig. 4 where each plot is made with the implementation of all the cuts sequentially on that variable, according to the cut flow given in Table II.  Table II prior to the cut on that variable The all steps of cut flow in the analysis for selecting the events are summarized in Table II. After applying the kinematical cuts discussed above, the effects of each cut on the reconstructed transverse momentum, p T and the obtained event yields is depicted in Fig. 5 for CP-conserving coupling, C BW /Λ 4 = 5 TeV −4 at L int = 10 ab −1 , as well as the other couplings have also similar behavior of the distributions.  Table II

IV. RESULTS
The study of finding the contribution of dim-8 operators transformed from the couplings of dim-6 operators for the 2 2ν final state process is carried out by using the p T distribution for each anomalous couplings with the implementation of all the cuts in Table II are applied up to the cut on that variable. The contribution of aT-GCs is presented by using an effective vertex function approach in Ref. [5]. Because of the aTGCs sensitivity have a potential to each out the high−p T sector, the p T > 110 GeV bins of the Fig. 6 are taken into account   Table III. tematic error for finding 95% C.L. bounds on the each couplings. This χ 2 function is defined as follows where N N P i is for the total number of events in the existence of effective couplings, N B i is total number of events of the corresponding SM backgrounds in ith bin of the p T distribution, ∆ i = δ 2 sys + 1/N B i is including the systematic (δ sys ) and statistical errors in each bin.
The presence of aNTGCs will give rise to enhance the yield of events at p T distributions of the νν final state of the ZZ process. The bounds on possible contributions from aNTGCs are obtained by using this distribution. To examine the viability of the EFT approach, one needs to require the lowest value of the coefficients to set the operator scale Λ beyond the reach of the kinematical range of the distributions in order for the EFT approach not to break down. The coefficients of the dim-8 operators could be related to the new physics characteristic scale Λ [15]. An upper limit can be enhance the new physics scale Λ using the fact that the fundamental theory is strongly coupled. We find Λ < 4πv √ s ∼ 17.5 TeV under the assumption of the couplings C = O(1). This upper bound is not violated in this analysis as we have m < 1.2 TeV for the kinematic range of invariant mass distributions.
Analyzing of ZZ production with 2 2ν in the final state, the number of signal events and one-parameter χ 2 results for each couplings varied with integrated luminosity from 1 ab −1 to 30 ab −1 . In the analysis, only one coupling at a time is varied from its SM value. The estimated results from χ 2 analysis of the couplings describing aTGC interactions of neutral gauge bosons. The coefficients of the operators denoted as C BW /Λ 4 , C W W /Λ 4 , C BW /Λ 4 and C BB /Λ 4 are given in Fig. 7. The obtained of one-dimensional 95% C.L. bounds at L int = 10 ab −1 with and without including the effects of systematic errors on the limits are summarized in Table IV assuming that any excess in signal over background expected solely to contribution of C BW /Λ 4 , C W W /Λ 4 , C BW /Λ 4 or C BB /Λ 4 couplings.

V. CONCLUSION
A phenomenological cut based study for searching the bounds of dim-8 aNTG CP-conserving C BW /Λ 4 and CPviolating C W W /Λ 4 , C BW /Λ 4 and C BB /Λ 4 dim-8 aNTG couplings via ZZ → νν (where = e or µ) production at the FCC-hh is summarized in this paper. When we compare the obtained bounds of dim-8 aNTG couplings at 95% C.L. with latest results of LHC [18], the sensitivity of each aNTG couplings is improved. The obtained results without systematic error, 53% (C BW /Λ 4 ), 76% (C W W /Λ 4 ), 81% ( C BW /Λ 4 ) and 52% (C BB /Λ 4 ), are better than the current phenomenological study [19] which is done for the process pp → ZZ → 4 at FCC-hh with an integrated luminosity L int = 10 fb −1 .
Even with 3% systematic errors, the obtained limits for FCC-hh are comparable or better than current LHC results. The obtained limits on aNTG couplings from this study would be to the advantage of the high luminosity when the systematic uncertainties are well reduced below 1%. These are current upper bounds on aNTG couplings.