# Search for Anomalous QuarticZZγγ Couplings in Photon-Photon Collisions

Authors: M. Köksal; V. Arı; A. Senol
Journal: Advances in High Energy Physics
 (2016)

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## Abstract

The self-couplings of the electroweak gauge bosons are completely specified by the non-Abelian gauge nature of the Standard Model (SM). The direct study of these couplings provides a significant opportunity to test the validity of the SM and the existence of new physics beyond the SM up to the high energy scale. For this reason, we investigate the potential of the processesγγ→ZZ, e-γ→e-γ⁎γ→e-ZZ,  and e+e-→e+γ⁎γ⁎e-→e+ZZe- to examine the anomalous quartic couplings of ZZγγ vertex at the Compact Linear Collider (CLIC) with center-of-mass energy 3 TeV. We calculate 95% confidence level sensitivities on the dimension-8 parameters with various values of the integrated luminosity. We show that the best bounds on the anomalous fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings arising from γγ→ZZ process among those three processes at center-of-mass energy of 3 TeV and integrated luminosity of Lint=2000 fb−1 are found to be [-3.30;3.30]×10-3 TeV−4, [-1.20;1.20]×10-2 TeV−4, [-3.40;3.40]×10-3 TeV−4, and [-1.80;1.80]×10-3 TeV−4, respectively.


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## Body

## 1. Introduction

The SM of particle physics has been tested with a lot of different experiments for decades and it is proven to be extremely successful. In addition, the discovery of all the particles predicted by the SM has been completed together with the ultimate discovery of the approximately 125 GeV Higgs boson in 2012 at the Large Hadron Collider (LHC) [1, 2]. However, we need new physics beyond the SM to find answers to some fundamental questions, such as the strong CP problem, neutrino oscillations, and matter-antimatter asymmetry in the universe. The self-interactions of electroweak gauge bosons are important and more sensitive for new physics beyond the SM. The structure of gauge boson self-interactions is completely determined by the non-Abelian SU(2)L⊗U(1)Y gauge symmetry in the SM. Contributions to these interactions, beyond those coming from the SM, will be a supporting evidence of probable new physics. It can be examined in a model independent way via the effective Lagrangian approach. Such an approach is parameterized by high-dimensional operators which induce anomalous quartic gauge couplings that modify the interactions between the electroweak gauge bosons.In writing effective operators associated with genuinely quartic couplings we employ the formalism of [3, 4]. Imposing global SU(2)L symmetry and local U(1)Y symmetry, dimension-6 effective Lagrangian for the ZZγγ coupling is given by(1)L=L0+Lc,L0=-πα4a0Λ2FμνFμνWαiWiα,Lc=-πα4acΛ2FμαFμβWiαWβi,where Fμν=∂μAν-∂νAμ is the tensor for electromagnetic field tensor, a0,c are the dimensionless anomalous quartic coupling constants, and Λ is a mass-dimension parameter associated with the scale of new physics.The anomalous quartic gauge couplings come out also from dimension-8 operators. There are three classes of operators containing either covariant derivatives of Higgs doublet (DμΦ) only, or two field strength tensors and two DμΦ, or field strength tensors only. The first class operators contain anomalous quartic gauge couplings involving only massive vector boson. We will not examine them since these operators contain only quartic W+W-W+W-, W+W-ZZ, and ZZZZ interactions. In the second class, eight anomalous quartic gauge boson couplings are given by [5–7](2)LM0=fM0Λ4TrWμνWμν×DβΦ†DβΦ,LM1=fM1Λ4TrWμνWνβ×DβΦ†DμΦ,LM2=fM2Λ4BμνBμν×DβΦ†DβΦ,LM3=fM3Λ4BμνBνβ×DβΦ†DμΦ,LM4=fM4Λ4DμΦ†WβνDμΦ×Bβν,LM5=fM5Λ4DμΦ†WβνDνΦ×Bβμ,LM6=fM6Λ4DμΦ†WβνWβνDμΦ,LM7=fM7Λ4DμΦ†WβνWβμDνΦ,where the field strength tensor of the SU(2) (Wμν) and U(1) (Bμν) is given by (3)Wμν=i2gτi∂μWνi-∂νWμi+gϵijkWμjWνk,Bμν=i2g′∂μBν-∂νBμ.Here, τi(i=1,2,3) are the SU(2) generators, g=e/sinθW, g′=g/cosθW, e is the unit of electric charge, and θW is the Weinberg angle. The dimension-6 operators can be expressed simply in terms of dimension-8 operators due to their similar Lorentz structures. The following expressions show the relations between the fMi couplings for the ZZγγ vertex and a0 and the ac couplings, needed to compare with the LEP results:(4)fM0Λ4=a0Λ21g2v2,fM1Λ4=-acΛ21g2v2,fM2Λ4=a0Λ22g2v2,fM3Λ4=-acΛ22g2v2,fM4Λ4=±a0Λ21g2v2,fM5Λ4=±acΛ22g2v2,fM6Λ4=a0Λ22g2v2,fM7Λ4=acΛ22g2v2.The operators containing four field strength tensors lead to quartic anomalous couplings are as follows:(5)LT0=fT0Λ4TrWμνWμν×TrWαβWαβ,LT1=fT1Λ4TrWανWμβ×TrWμβWαν,LT2=fT2Λ4TrWαμWμβ×TrWβνWνα,LT5=fT5Λ4TrWμνWμν×BαβBαβ,LT6=fT6Λ4TrWανWμβ×BμβBαν,LT7=fT7Λ4TrWαμWμβ×BβνBνα,LT8=fT8Λ4BμνBμνBαβBαβ,LT9=fT9Λ4BαμBμβBβνBνα,where fT0, fT1, fT2, fT5, fT6, fT7, fT8, and fT9 are dimensionless parameters which have no dimensions-6 analogue.The experimental 95% CL bounds on dimension-6ZZγγ couplings at the LEP by OPAL collaboration through the process e+e-→Zγγ→qq-γγ are [8](6)-0.007GeV-2<a0Λ2<0.023GeV-2,-0.029GeV-2<acΛ2<0.029GeV-2.The 95% CL one-dimensional bounds on dimension-8 parameters at the LHC by ATLAS collaboration throughqq-→Zγγ with an integrated luminosity of 20.3 fb−1 at s=8 TeV [9] are(7)-1.6×104TeV-4<fM2Λ4<1.6×104TeV-4,-2.9×104TeV-4<fM3Λ4<2.7×104TeV-4,-0.86×102TeV-4<fT0Λ4<1.03×102TeV-4,-0.69×103TeV-4<fT5Λ4<0.68×103TeV-4,-0.74×104TeV-4<fT9Λ4<0.74×104TeV-4.In the literature, the anomalous quarticZZγγ couplings have been performed with Monte-Carlo studies at the linear e+e- colliders via the processes e+e-→Zγγ [10, 11], e+e-→ZZγ [12], e+e-→qq-γγ [13], e+e-→e+γ∗e-→e+ZZe- [14], eγ→ZZe [15], eγ→Zγe [16], e+e-→e+γ∗γ∗e-→e+ZZe- [14], and γγ→WWZ [17]. For the hadron colliders, studies have been done on anomalous quartic ZZγγ couplings via the processes pp-→Zγγ [18], pp(p-)→γγll [19], pp→pγ∗γ∗p→pZZp [20–23], pp→pγ∗p→pZZqX [24], pp→pγ∗p→pγZqX [25], and pp→qqγll [26].


## 2. Photon Colliders

The LHC may not be an ideal platform to study new physics beyond the SM because of remnants arising from the strong interactions. On the other hand, the linear colliders usually supply a cleaner environment with respect to the hadron colliders. The CLIC is one of the most popular linear collider designs, and it will operate in three different center-of-mass energy stages. Probable operating scenarios of CLIC are planned with an integrated luminosity of500 fb−1 at 0.35 TeV, 1500 fb−1 at 1.4 TeV, and 2000 fb−1 at 3 TeV collision energy [27]. Having high luminosity and energy is extremely significant in terms of new physics research. Particularly, the anomalous quartic gauge couplings are described by means of high-dimensional effective Lagrangian which have very strong energy dependence. For this reason, the sensitivity to the anomalous couplings increases with energy much faster than the sensitivity to the SM ones, and they can be measured with better precision. Also, the e-e+ colliders are more likely to produce three or more massive gauge bosons in the final states of the studying processes. As a result, these colliders will provide an occasion to investigate the anomalous quartic gauge boson couplings.The expected design of the future linear collider will include operation also ineγ and γγ modes. In eγ and γγ processes, real photon beams can be generated by converting the incoming e- and e+ beams into photon beams through the Compton backscattering mechanism. The maximum collision energy is expected to be 80% for γγ collision and 90% for eγ collision of the original e+e- collision energy. However, the expected luminosities are 15% for γγ collision and 39% for eγ collision of the e+e- luminosities [28]. Also when using directly the lepton beams, quasi-real photons will be radiated at the interaction allowing for processes like eγ∗, γγ∗, and γ∗γ∗ to occur [29–34]. Alternatively, a γ∗ photon emitted from either of the incoming leptons can interact with a laser photon backscattered from the other lepton beam, and the subprocess γγ∗→ZZ can take place. Hence, we calculate the process eγ→eγ∗γ→eZZ by integrating the cross section for the subprocess γγ∗→ZZ over the γ∗ flux. Furthermore, γ∗ photons emitted from both lepton beams can collide with each other and the subprocess γ∗γ∗→ZZ can be produced, and the cross section for the full process ee→eγ∗γ∗e→eZZe is calculated by integrating the cross section for the subprocess γ∗γ∗→ZZ over both γ∗ fluxes. The quasi-real γ∗ flux in γγ∗ and γ∗γ∗ collisions is defined by the Weizsacker-Williams approximation (WWA). In the WWA, the electroproduction processes include a small angle of charged particle scattering. The virtuality of γ∗ photons emitted by the scattering particle is very small. Hence, they are supposed to be almost real. There is a possibility to reduce the process of electroproduction to the photoproduction described by the following photon spectrum [32]:(8)fx,Qmax=α2π1+1-x2log⁡QmaxQmin-2mex21Qmin-1Qmax,where me is mass of the scattering particle, Qmin=me2x/(1-x), and x=Eγ/E. Eγ and E are energy of photon and energy of scattered electron (positron), respectively. Many examples of investigation of possible new physics beyond the SM through photon-induced processes using the WWA are available in the literature [24, 35–61].


## 3.ZZ Production at γγ, γ∗γ∗, and γ∗γ Collisions

In this section we will display the differential cross sections by considering the contributions of all three types of collisions separately,γγ, γ∗γ∗, and γ∗γ, for the ZZ productions through the process γγ→ZZ and the subprocesses γ∗γ∗→ZZ and γγ∗→ZZ. The representative leading order Feynman diagrams of these process are given in Figure 1. The dimension-8 anomalous interaction vertices in (2) and (5) are implemented in FeynRules [62] and passed to MadGraph 5 [63] framework by means of the UFO model [64].Figure 1
Tree-level Feynman diagrams for the processes (a)γγ→ZZ, (b) e-γ→e-γ∗γ→e-ZZ, and (c) e+γ∗γ∗e-→e+ZZe-.
(a) (b) (c)


### 3.1.γγCollision

The total cross section for the processγγ→ZZ has been calculated by using real photon spectrum produced by Compton backscattering of laser beam off the high energy electron beam. We show the total cross section of the process γγ→ZZ depending on the dimension-8 anomalous couplings fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 for s = 3 TeV in Figure 2. In addition to these, the total cross sections as function of anomalous quartic couplings assuming Λ = 1 TeV are given in Table 1. In Figure 2, the cross sections depending on the anomalous quartic gauge couplings were obtained by varying only one of the anomalous couplings at a time while the others were fixed to zero. From these figures we can see that the contribution comes from fT9/Λ4 coupling to the cross section which grows rapidly while fM2/Λ4, fM3/Λ4, and fT0/Λ4 couplings are slowly varying. Hence the bounds on fT9/Λ4 coupling are expected to be more sensitive in accordance with fM2/Λ4, fM3/Λ4, and fT0/Λ4. Similarly, sensitivities on fM2/Λ4 and fT0/Λ4 couplings are expected to be more restrictive than sensitivities on fM3/Λ4.Table 1
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings assuming Λ = 1 TeV for the processes γγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe- at CLIC with s=3 TeV.
Modes  Total cross sections (pb) γ γ 31.0fM22 2.21fM32 28.36fT02 103.5fT92 e γ 1.96fM22 0.14fM32 1.80fT02 6.60fT92 e + e - 1.24 × 1 0 - 1 f M 2 2 8.86 × 1 0 - 3 f M 3 2 1.14 × 1 0 - 1 f T 0 2 4.19×10-1fT92Figure 2
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process γγ→ZZ at CLIC with s=3 TeV.


### 3.2.γ∗γ∗ Collision

Theγ∗γ∗→ZZ is generated via the quasi-real photons emitted from both lepton beams collision with each other and participates as a subprocess in the main process e-e+→e-γ∗γ∗e+→e-ZZe+. When calculating the total cross sections for this process, we take into account the equivalent photon approximation structure function using the improved Weizsaecker-Williams formula which is embedded in MadGraph. The total cross sections of the process as a function of fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 for s = 3 TeV are given in Figure 3 and tabulated in Table 1 assuming Λ=1 TeV.Figure 3
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process e+e-→e+γ∗γ∗e-→e+ZZe- at CLIC with s=3 TeV.


### 3.3.γγ∗ Collision

One of the operating mode of the conventionale+e- machine is the eγ mode. This mode includes γγ∗ collision of a Weisaczker-Willams photon (γ∗) emitted from the incoming leptons and the laser backscattered photon (γ). Thus, the reaction γγ∗→ZZ participates as a subprocess in the main process e-γ→e-γ∗γ→e-ZZ. In Figure 4, we plot the total cross section of the process e-γ→e-γ∗γ→e-ZZ as a function of dimension-8 couplings for s = 3 TeV. Also, the total cross sections as function of anomalous quartic couplings assuming Λ = 1 TeV are given in Table 1.Figure 4
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process e-γ→e-γ∗γ→e-ZZ at CLIC with s=3 TeV.


## 3.1.γγCollision

The total cross section for the processγγ→ZZ has been calculated by using real photon spectrum produced by Compton backscattering of laser beam off the high energy electron beam. We show the total cross section of the process γγ→ZZ depending on the dimension-8 anomalous couplings fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 for s = 3 TeV in Figure 2. In addition to these, the total cross sections as function of anomalous quartic couplings assuming Λ = 1 TeV are given in Table 1. In Figure 2, the cross sections depending on the anomalous quartic gauge couplings were obtained by varying only one of the anomalous couplings at a time while the others were fixed to zero. From these figures we can see that the contribution comes from fT9/Λ4 coupling to the cross section which grows rapidly while fM2/Λ4, fM3/Λ4, and fT0/Λ4 couplings are slowly varying. Hence the bounds on fT9/Λ4 coupling are expected to be more sensitive in accordance with fM2/Λ4, fM3/Λ4, and fT0/Λ4. Similarly, sensitivities on fM2/Λ4 and fT0/Λ4 couplings are expected to be more restrictive than sensitivities on fM3/Λ4.Table 1
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings assuming Λ = 1 TeV for the processes γγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe- at CLIC with s=3 TeV.
Modes  Total cross sections (pb) γ γ 31.0fM22 2.21fM32 28.36fT02 103.5fT92 e γ 1.96fM22 0.14fM32 1.80fT02 6.60fT92 e + e - 1.24 × 1 0 - 1 f M 2 2 8.86 × 1 0 - 3 f M 3 2 1.14 × 1 0 - 1 f T 0 2 4.19×10-1fT92Figure 2
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process γγ→ZZ at CLIC with s=3 TeV.


## 3.2.γ∗γ∗ Collision

Theγ∗γ∗→ZZ is generated via the quasi-real photons emitted from both lepton beams collision with each other and participates as a subprocess in the main process e-e+→e-γ∗γ∗e+→e-ZZe+. When calculating the total cross sections for this process, we take into account the equivalent photon approximation structure function using the improved Weizsaecker-Williams formula which is embedded in MadGraph. The total cross sections of the process as a function of fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 for s = 3 TeV are given in Figure 3 and tabulated in Table 1 assuming Λ=1 TeV.Figure 3
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process e+e-→e+γ∗γ∗e-→e+ZZe- at CLIC with s=3 TeV.


## 3.3.γγ∗ Collision

One of the operating mode of the conventionale+e- machine is the eγ mode. This mode includes γγ∗ collision of a Weisaczker-Willams photon (γ∗) emitted from the incoming leptons and the laser backscattered photon (γ). Thus, the reaction γγ∗→ZZ participates as a subprocess in the main process e-γ→e-γ∗γ→e-ZZ. In Figure 4, we plot the total cross section of the process e-γ→e-γ∗γ→e-ZZ as a function of dimension-8 couplings for s = 3 TeV. Also, the total cross sections as function of anomalous quartic couplings assuming Λ = 1 TeV are given in Table 1.Figure 4
The total cross sections as function of anomalousfM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for the process e-γ→e-γ∗γ→e-ZZ at CLIC with s=3 TeV.


## 4. Bounds on Anomalous Quartic Couplings

The SM cross section of the processesγγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe- is quite small, because the process γγ→ZZ and the subprocesses γ∗γ→ZZ and γ∗γ∗→ZZ are not allowed at the tree level. They are only allowed at loop level and can be neglected. On the other hand, as stated in [65], the SM background and their interference contributions of the examined processes may be important for low center-of-mass energies such as 0.35 TeV and 1.4 TeV. However, the effect of the one-loop SM cross section at s=3 TeV of these processes is expected to give relatively small contributions and it can be neglected. For this reason, we analysis anomalous ZZγγ quartic couplings only at s=3 TeV for three processes. Therefore, in the course of statistical analysis, the bounds of all anomalous quartic couplings at 95% CL are calculated using the Poisson statistics test since the number of SM background events of the examined processes is expected to be negligible events for the various values of the luminosities at s=3 TeV. In this case, the upper bounds of number of events Nup at the 95% CL can be calculated from the following formula: (9)∑k=0NobsPPoissonNup;k=1-CL,where Nobs is the number of observed events and the value of Nup can be obtained with respect to the value of the number of observed events. For calculating the limits on anomalous quartic gauge couplings in case there is no signal, Nobs = 0, and then Nup is always 3, for 95% CL. This upper limit on the number of events is translated, in each case separately, to an upper/lower limit on the anomalous quartic gauge couplings, using the cross section dependence on the anomalous quartic gauge couplings at the corresponding energy and multiplying the cross section by the branching ratio for leptonic Z decays and by the corresponding luminosity. The bounds at 95% CL on these couplings at the CLIC with s = 3 TeV for various integrated luminosities are shown in Figures 5–7 for the examined processes. Here we consider that only one of the anomalous couplings changes at any time.Figure 5
95% CL sensitivity bounds offM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for various values of integrated luminosities and s=3 TeV through the process γγ→ZZ.Figure 6
95% CL sensitivity bounds offM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for various values of integrated luminosities and s=3 TeV through the process e-γ→e-γ∗γ→e-ZZ.Figure 7
95% CL sensitivity bounds offM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for various values of integrated luminosities and s=3 TeV through the process e+e-→e+γ∗γ∗e-→e+ZZe-.As can be seen from Figure5, the sensitivity bounds of fM2/Λ4 and fM3/Λ4 couplings obtained from the process γγ→ZZ with s = 3 TeV and Lint=2000 fb−1 are calculated as [-3.30;3.30]×10-3 TeV−4 and [-1.20;1.20]×10-2 TeV−4 which are seven and six orders of magnitude better than the experimental bounds of the LHC, respectively. The expected best sensitivities on fT0/Λ4 and fT9/Λ4 couplings in Figure 5 are far beyond the sensitivities of the LHC. As can be seen from Table 2, when the luminosity reduction factor is taken into account, these limits become [-8.45;8.45]×10-3 TeV−4 and [-3.17;3.17]×10-2 TeV−4, respectively. So, the sensitivity of the limits calculated using luminosity reduction factors decreases by about 2.5 times for γγ option and 1.6 times for eγ option in e+e- collisions.Table 2
95% CL sensitivity bounds ofa0/Λ2, ac/Λ2, fM2/Λ4, fM3/Λ4, fT0/Λ4, and fT9/Λ4 couplings for 2000 fb−1 integrated luminosity and s = 3 TeV through the processes γγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe-. The values in the parentheses are calculated limits using the luminosity reduction factor.
Couplings γ γ mode e γ mode e + e - mode a 0 / Λ 2 (TeV−2) [ - 4.27 ; 4.27 ] × 1 0 - 5 [ - 1.68 ; 1.68 ] × 1 0 - 4 [ - 6.68 ; 6.68 ] × 1 0 - 4 ( [ - 1.09 ; 1.09 ] × 1 0 - 4 ) ( [ - 2.69 ; 2.69 ] × 1 0 - 4 ) a c / Λ 2 (TeV−2) [ - 1.55 ; 1.55 ] × 1 0 - 4 [ - 6.29 ; 6.29 ] × 1 0 - 4 [ - 2.46 ; 2.46 ] × 1 0 - 3 ( [ - 4.11 ; 4.11 ] × 1 0 - 4 ) ( [ - 1.01 ; 1.01 ] × 1 0 - 3 ) f M 2 / Λ 4 (TeV−4) [ - 3.30 ; 3.30 ] × 1 0 - 3 [ - 1.30 ; 1.30 ] × 1 0 - 2 [ - 5.16 ; 5.16 ] × 1 0 - 2 ( [ - 8.45 ; 8.45 ] × 1 0 - 3 ) ( [ - 2.08 ; 2.08 ] × 1 0 - 2 ) f M 3 / Λ 4 (TeV−4) [ - 1.20 ; 1.20 ] × 1 0 - 2 [ - 4.86 ; 4.86 ] × 1 0 - 2 [ - 1.90 ; 1.90 ] × 1 0 - 1 ( [ - 3.17 ; 3.17 ] × 1 0 - 2 ) ( [ - 7.79 ; 7.79 ] × 1 0 - 2 ) f T 0 / Λ 4 (TeV−4) [ - 3.40 ; 3.40 ] × 1 0 - 3 [ - 1.36 ; 1.36 ] × 1 0 - 2 [ - 5.39 ; 5.39 ] × 1 0 - 2 ( [ - 8.83 ; 8.83 ] × 1 0 - 3 ) ( [ - 2.17 ; 2.17 ] × 1 0 - 2 ) f T 9 / Λ 4 (TeV−4) [ - 1.80 ; 1.80 ] × 1 0 - 3 [ - 7.09 ; 7.09 ] × 1 0 - 3 [ - 2.81 ; 2.81 ] × 1 0 - 2 ( [ - 8.83 ; 8.83 ] × 1 0 - 3 ) ( [ - 1.14 ; 1.14 ] × 1 0 - 2 )We compare our results with the best bounds obtained from the phenomenological studies of the LHC, future hadron, and linear colliders in the literature. The bounds ona0/Λ2 and ac/Λ2 couplings arising from dimension-6 operators have been obtained by [20, 66]. For 95% CL with integrated luminosity of 200 fb−1 at s=14 TeV at the LHC, the sensitivities on the anomalous couplings are calculated as [-1.1;1.1] TeV−2 and [-4.8;4.8] TeV−2, respectively. However, the best sensitivities on a0/Λ2 and ac/Λ2 couplings for Lint=590 fb−1 at s=3 TeV at the CLIC are at the order of 10−2 TeV−2 [14]. Also, [5, 67] have investigated the couplings of dimension-8 operators at 95% CL with integrated luminosity of 300 fb−1 at s=14 TeV and 3000 fb−1 at s=14 TeV, 33 TeV, and 100 TeV at the LHC and future hadron colliders. The bounds on the couplings arising from dimension-8 operators are given fM2/Λ4 = 25 TeV−4 and fM3/Λ4 = 38 TeV−4.In Table2, we show the best sensitivity bounds at 95% CL of fM2,3/Λ4 and a0,c/Λ2 couplings for three processes with integrated luminosity 2000 fb−1 at s=3 TeV. As can be seen in Table 2, our best sensitivities on a0,c/Λ2 couplings by examining the process γγ→ZZ are about 105 times better than the sensitivities calculated in [20, 66]. Our bounds can set more stringent sensitivity by three orders of magnitude with respect to the best sensitivity derived from the CLIC with s=3 TeV. Finally, we can understand from Table 2 that the best bounds obtained through the process γγ→ZZ with integrated luminosity 2000 fb−1 at s=3 TeV improve the sensitivities of fM2/Λ4 and fM3/Λ4 couplings by up to a factor of 104 compared to [5, 67]. However, we compare our results with the sensitivities of [67] which investigates phenomenologically fT9/Λ4 coupling via pp→ZZ+2j→4l+2j process at s = 14 (33)  TeV with 300 (3000) fb−1 luminosity. The bound on fT9/Λ4 coupling at s = 33 TeV with Lint=3000 fb−1 is [-2.50;2.50] TeV−4 which is up to a factor of 103 worse than our best bound. However, it can be seen from Figure 6 that bounds on fT9/Λ4 coupling obtained from the process e-γ→e-γ∗γ→e-ZZ are more restrictive than the bounds on fM2/Λ4, fM3/Λ4, and fT0/Λ4 couplings. The best sensitivities obtained for four different couplings from the process γγ→ZZ in Figure 5 are approximately an order of magnitude more restrictive with respect to the main process e+e-→e+γ∗γ∗e-→e+ZZe- in Figure 7 which is obtained by integrating the cross section for the subprocess γ∗γ∗→ZZ over the effective photon luminosity. Although the luminosity reduction factor is taken into account in γγ and eγ collision modes, the results show that γγ collisions give the best bounds to test anomalous quartic gauge couplings with respect to γ∗γ∗ and γγ∗ collisions. Principally, the sensitivity of the processes to anomalous couplings rapidly increases with the center-of-mass energy and the luminosity.


## 5. Conclusions

CLIC is envisaged as a high energye+e- collider having very clean experimental conditions and being free from strong interactions with respect to the LHC. In addition, the number of SM events vanishes for γγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe- processes. Therefore, the observation of a few events at the final state of such processes would be an important sign for anomalous quartic couplings beyond the SM. For these reasons, we have estimated the improvement of sensitivity to anomalous quartic ZZγγ couplings with dimension-8 as function of collider energies and luminosities through the processes γγ→ZZ, e-γ→e-γ∗γ→e-ZZ, and e+e-→e+γ∗γ∗e-→e+ZZe-. As a result, the CLIC as photon-photon collider provides an ideal platform to examine anomalous quartic ZZγγ gauge couplings at high energies and luminosities.



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