The projections on $ZZ\gamma$ and $Z\gamma\gamma$ couplings via $\nu\bar \nu \gamma$ production in HL-LHC and HE-LHC

We investigate the sensitivity of the anomalous dimension-8 neutral triple gauge couplings via process $pp\to \nu\nu\gamma$ with fast detector simulation including pile-up effects for the post LHC experiments. The transverse momentum of the final state photon and missing energy transverse distributions are considered in the analysis. We obtain the sensitivity to the $C_{\widetilde B W}/\Lambda^4$, $C_{B B}/\Lambda^4$, $C_{WW}/\Lambda^4$ and $C_{BW}/\Lambda^4$ couplings at HL-LHC and HE-LHC with an integrated luminosity of 3 ab$^{-1}$ and 15 ab$^{-1}$, respectively. Finally, our numerical results show that one can reach the constraints at 95\% confidence level without systematic error on $C_{\widetilde BW}/\Lambda^4$, $C_{B B}/\Lambda^4$, $C_{W W}/\Lambda^4$ and $C_{BW}/\Lambda^4$ couplings for HL-LHC (HE-LHC) as [-0.38;0.38] ([-0.12;0.12]), [-0.21;0.21]([-0.085;0.085]), [-1.08;1.08]([-0.38;0.38]) and [-0.48;0.48]([-0.25;0.25]), respectively. They are better than the experimental limits obtained by LHC.


I. INTRODUCTION
The Standard Model (SM) is a successful theory at describing the particle physics phenomena in reachable energy limits of current collider experiments. Nevertheless, the SM needs to be extended to explain some experimental and theoretical facts such as the electroweak scale-Planck scale hierarchy problem, the striking evidence of dark matter, the dynamic origin of the Higgs mechanism and non-zero neutrino masses. Any significant deviation from the expectation of SM has not been observed since the beginning of the LHC era. However, the explanation of physics beyond the SM can benefit from the High Luminosity LHC (HL-LHC) [1] and High Energy LHC (HE-LHC) [2] with novel technologies and approaches. These future considerations aim to extend direct and indirect sensitivities to new physics and discoveries not only by increasing luminosity and center of mass energy but also sensitive technologies involved in the detectors.
The progress in the understanding of the Higgs and gauge sector via the precision measurements can play key role in exploration of the new physics. A new range of luminosity and energy will provide valuable information to find new phenomena or set limits on various aspects of new physics models in coming years. In this work, we use well motivated effective field theory (EFT) to probe expected deviations on the neutral three-boson couplings from new physics.
We use a Lagrangian of the EFT including both SM interactions and neutral Triple Gauge Couplings (NTGC) obeying local U (1) EM and Lorentz symmetry as given in Ref. [3] where four operators with index i can be expressed as whereB µν is a dual B strength tensor. The following convention in the definitions of the operators are used: with σ I σ J = δ IJ /2 and These dimension-eight operators have four coefficients. The CB W /Λ 4 coefficient is CPconserving, while the others C BB /Λ 4 , C BW /Λ 4 , C W W /Λ 4 are CP-violating. As described in Ref. [3]., they can also be related to dimension-six operators of anomalous NTGC (aNTGC).
The dimension-six operators can have an effect on aNTGC at one-loop level (at the order O(αŝ/4πΛ 2 )) as they do not induce aNTGC at tree-level [3]. However, the tree level contributions from dimension-eight operators are of the order O(ŝ 2 /Λ 4 ). Therefore, one-loop contribution of the dim-6 operators can be ignored with respect to that of dim-8 operators The ATLAS collaboration sets the current experimental bounds on dimension-eight operators with a conversion from the coefficients of dimension-six operators for the process pp → ZZ → l + l − l + l − [4]. The production process of pp → Zγ → νν has already been searched in Ref. [5] at √ s = 13 TeV with L int =36.1 fb −1 . The results from these references are tabulated at a 95% C.L. in Table I. The constraints on dimension eight operatos in the pp → llγ and pp → ννγ processes have been studied for a 100 TeV center of mass energy collider (FCC-hh) [6]. In this analysis we focus on CP-conserving C BW /Λ 4 and CP-violating C BB /Λ 4 , C W W /Λ 4 ,C BW /Λ 4 couplings via pp → ννγ process in other post LHC considerations, namely HL-LHC and HE-LHC including pile-up effects. Z(νν)γ final state is selected due to its several advantages over the Z(ll)γ and Z(qq)γ final states. Even though Z decaying to quark-antiquark pair has a branching ratio of 69.9%, this channel is contaminated by a large multi-jet background. Z boson decays in 20% of the cases into neutrino pair while 10% into charged lepton-antilepton pairs. Therefore one can take advantages of the opportunity to study Zγ production in more energetic (higher E γ T ) region. In addition, this process is more sensitive to bosonic couplings. The tree level Feynman diagrams of the pp → ννγ process are shown in Fig are calculated at leading order including the transverse momentum ( p γ T >100 GeV) and pseudo-rapidity (η γ < 2.5) cuts for photons. In addition, one of the effective couplings is non-zero at a time, while the other couplings are fixed to zero. As it can be seen from Fig. 2, deviation from SM value of the anomalous cross section including C BW /Λ 4 ,C BB /Λ 4 couplings is larger than that for C W W /Λ 4 and C BW /Λ 4 in both HL-LHC and HE-LHC options. The cross sections values for the HE-LHC option are greater than for the HL-LHC option as one can expect due to higher center of mass energy. We will consider C BW , C BB , C BW and C W W couplings in the detailed analysis including detector and pile-up effects through ννγ production at HL-LHC and HE-LHC with 14 TeV and 27 TeV center of mass energy in the next section.

II. SIGNAL AND BACKGROUND ANALYSIS
The detailed analysis of effective dim-8 aNTGC couplings and SM contributions as well as interference between effective couplings and SM contribution is performed via pp → ννγ process. Approximately two million events are generated at LO partonic level in MadGraph5_aMC@NLO applying pseudo-rapidity (|η γ |< 2.5) and transverse momentum ( Since we focus on pp → ννγ process to search for sensitivity to the dimension-8 anomalous Zγγ and ZZγ couplings, at least one photon is required with non-zero missing energy transverse (MET) in the final state. One can expect to find distinctive properties of this process in the kinematic distributions of leading photon and MET. The p γ T distribution of leading photon (upper) and MET distribution (lower) for signal C BW /Λ 4 ,C BB /Λ 4 , C W W /Λ 4 and C BW /Λ 4 (left to right) couplings and corresponding SM background for pp → ννγ process at HL-LHC and HE-LHC are given in Fig. 3 and Fig. 4, respectively.  As it can be seen from Fig.3 and Fig. 4, the deviation of signal from the SM background for all couplings appears to be around 400 GeV for both p γ T and MET distributions. Therefore, we impose the following cuts p γ T > 400 GeV, MET > 400 GeV and |η γ |< 2.5 for further analysis.

III. RESULTS OF THE ANALYSIS
In order to obtain sensitivity of C BW /Λ 4 ,C BB /Λ 4 , C W W /Λ 4 and C BW /Λ 4 couplings via the pp → ννγ process, we use χ 2 method. The χ 2 function with and without a systematic error is defined as follows where N N P i is 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 γ T distributions, is the combined systematic (δ sys ) and statistical errors in each bin. Fig. 5 and respectively. Results compared with current ATLAS limits [5] are summarized in Fig.7.
For all couplings we obtained better limits than current experimental limits from LHC.
Furthermore, our obtained limits on C BW /Λ 4 and C W W /Λ 4 couplings at 27 TeV center of mass energy with an integrated luminosity 15 ab −1 are one order of magnitude better. Even including 3 % systematic error, our results are better for HE-LHC and comparable for HL-LHC. One can also perform the sensitivity of the dimension-8 couplings using tagged protons at hadron-hadron colliders as suggested in Ref. [13][14][15].  TeV. This upper bound is not violated in this analysis since we have p γ T < 800 GeV for the kinematical range of distributions related to the photon in the final state.