Research Article  Open Access
Search for Anomalous Quartic Couplings in PhotonPhoton Collisions
Abstract
The selfcouplings of the electroweak gauge bosons are completely specified by the nonAbelian 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 processes , , and to examine the anomalous quartic couplings of vertex at the Compact Linear Collider (CLIC) with centerofmass energy 3 TeV. We calculate confidence level sensitivities on the dimension8 parameters with various values of the integrated luminosity. We show that the best bounds on the anomalous , , , and couplings arising from process among those three processes at centerofmass energy of 3 TeV and integrated luminosity of fb^{−1} are found to be TeV^{−4}, TeV^{−4}, TeV^{−4}, and TeV^{−4}, respectively.
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 matterantimatter asymmetry in the universe. The selfinteractions of electroweak gauge bosons are important and more sensitive for new physics beyond the SM. The structure of gauge boson selfinteractions is completely determined by the nonAbelian 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 highdimensional 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 symmetry and local symmetry, dimension6 effective Lagrangian for the coupling is given bywhere is the tensor for electromagnetic field tensor, are the dimensionless anomalous quartic coupling constants, and is a massdimension parameter associated with the scale of new physics.
The anomalous quartic gauge couplings come out also from dimension8 operators. There are three classes of operators containing either covariant derivatives of Higgs doublet () only, or two field strength tensors and two , 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 , , and interactions. In the second class, eight anomalous quartic gauge boson couplings are given by [5–7]where the field strength tensor of the () and () is given by Here, are the generators, , , is the unit of electric charge, and is the Weinberg angle. The dimension6 operators can be expressed simply in terms of dimension8 operators due to their similar Lorentz structures. The following expressions show the relations between the couplings for the vertex and and the couplings, needed to compare with the LEP results:
The operators containing four field strength tensors lead to quartic anomalous couplings are as follows: where , , , , , , , and are dimensionless parameters which have no dimensions6 analogue.
The experimental 95% CL bounds on dimension6 couplings at the LEP by OPAL collaboration through the process are [8]
The 95% CL onedimensional bounds on dimension8 parameters at the LHC by ATLAS collaboration through with an integrated luminosity of 20.3 fb^{−1} at TeV [9] are
In the literature, the anomalous quartic couplings have been performed with MonteCarlo studies at the linear colliders via the processes [10, 11], [12], [13], [14], [15], [16], [14], and [17]. For the hadron colliders, studies have been done on anomalous quartic couplings via the processes [18], [19], [20–23], [24], [25], and [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 centerofmass energy stages. Probable operating scenarios of CLIC are planned with an integrated luminosity of fb^{−1} at TeV, fb^{−1} at TeV, and fb^{−1} at 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 highdimensional 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 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 in and modes. In and processes, real photon beams can be generated by converting the incoming and beams into photon beams through the Compton backscattering mechanism. The maximum collision energy is expected to be 80% for collision and 90% for collision of the original collision energy. However, the expected luminosities are 15% for collision and 39% for collision of the luminosities [28]. Also when using directly the lepton beams, quasireal photons will be radiated at the interaction allowing for processes like , , and to occur [29–34]. Alternatively, a photon emitted from either of the incoming leptons can interact with a laser photon backscattered from the other lepton beam, and the subprocess can take place. Hence, we calculate the process by integrating the cross section for the subprocess over the flux. Furthermore, photons emitted from both lepton beams can collide with each other and the subprocess can be produced, and the cross section for the full process is calculated by integrating the cross section for the subprocess over both fluxes. The quasireal flux in and collisions is defined by the WeizsackerWilliams approximation (WWA). In the WWA, the electroproduction processes include a small angle of charged particle scattering. The virtuality of 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]:where is mass of the scattering particle, , and . and are energy of photon and energy of scattered electron (positron), respectively. Many examples of investigation of possible new physics beyond the SM through photoninduced processes using the WWA are available in the literature [24, 35–61].
3. Production at , , and Collisions
In this section we will display the differential cross sections by considering the contributions of all three types of collisions separately, , , and , for the productions through the process and the subprocesses and . The representative leading order Feynman diagrams of these process are given in Figure 1. The dimension8 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].
(a)
(b)
(c)
3.1. Collision
The total cross section for the process 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 depending on the dimension8 anomalous couplings , , , and for = 3 TeV in Figure 2. In addition to these, the total cross sections as function of anomalous quartic couplings assuming = 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 coupling to the cross section which grows rapidly while , , and couplings are slowly varying. Hence the bounds on coupling are expected to be more sensitive in accordance with , , and . Similarly, sensitivities on and couplings are expected to be more restrictive than sensitivities on .

3.2. Collision
The is generated via the quasireal photons emitted from both lepton beams collision with each other and participates as a subprocess in the main process . When calculating the total cross sections for this process, we take into account the equivalent photon approximation structure function using the improved WeizsaeckerWilliams formula which is embedded in MadGraph. The total cross sections of the process as a function of , , , and for = 3 TeV are given in Figure 3 and tabulated in Table 1 assuming TeV.
3.3. Collision
One of the operating mode of the conventional machine is the mode. This mode includes collision of a WeisaczkerWillams photon () emitted from the incoming leptons and the laser backscattered photon (). Thus, the reaction participates as a subprocess in the main process . In Figure 4, we plot the total cross section of the process as a function of dimension8 couplings for = 3 TeV. Also, the total cross sections as function of anomalous quartic couplings assuming = 1 TeV are given in Table 1.
4. Bounds on Anomalous Quartic Couplings
The SM cross section of the processes , , and is quite small, because the process and the subprocesses and 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 centerofmass energies such as 0.35 TeV and 1.4 TeV. However, the effect of the oneloop SM cross section at TeV of these processes is expected to give relatively small contributions and it can be neglected. For this reason, we analysis anomalous quartic couplings only at 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 TeV. In this case, the upper bounds of number of events at the 95% CL can be calculated from the following formula: where is the number of observed events and the value of 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, = 0, and then 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 decays and by the corresponding luminosity. The bounds at 95% CL on these couplings at the CLIC with = 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.
As can be seen from Figure 5, the sensitivity bounds of and couplings obtained from the process with = 3 TeV and fb^{−1} are calculated as TeV^{−4} and TeV^{−4} which are seven and six orders of magnitude better than the experimental bounds of the LHC, respectively. The expected best sensitivities on and 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 TeV^{−4} and TeV^{−4}, respectively. So, the sensitivity of the limits calculated using luminosity reduction factors decreases by about 2.5 times for option and 1.6 times for option in collisions.

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 on and couplings arising from dimension6 operators have been obtained by [20, 66]. For 95% CL with integrated luminosity of 200 fb^{−1} at TeV at the LHC, the sensitivities on the anomalous couplings are calculated as TeV^{−2} and TeV^{−2}, respectively. However, the best sensitivities on and couplings for fb^{−1} at TeV at the CLIC are at the order of 10^{−2} TeV^{−2} [14]. Also, [5, 67] have investigated the couplings of dimension8 operators at 95% CL with integrated luminosity of 300 fb^{−1} at TeV and 3000 fb^{−1} at TeV, 33 TeV, and 100 TeV at the LHC and future hadron colliders. The bounds on the couplings arising from dimension8 operators are given = 25 TeV^{−4} and = 38 TeV^{−4}.
In Table 2, we show the best sensitivity bounds at 95% CL of and couplings for three processes with integrated luminosity 2000 fb^{−1} at TeV. As can be seen in Table 2, our best sensitivities on couplings by examining the process are about 10^{5} 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 TeV. Finally, we can understand from Table 2 that the best bounds obtained through the process with integrated luminosity 2000 fb^{−1} at TeV improve the sensitivities of and couplings by up to a factor of 10^{4} compared to [5, 67]. However, we compare our results with the sensitivities of [67] which investigates phenomenologically coupling via process at = 14 TeV with 300 (3000) fb^{−1} luminosity. The bound on coupling at = 33 TeV with fb^{−1} is TeV^{−4} which is up to a factor of 10^{3} worse than our best bound. However, it can be seen from Figure 6 that bounds on coupling obtained from the process are more restrictive than the bounds on , , and couplings. The best sensitivities obtained for four different couplings from the process in Figure 5 are approximately an order of magnitude more restrictive with respect to the main process in Figure 7 which is obtained by integrating the cross section for the subprocess over the effective photon luminosity. Although the luminosity reduction factor is taken into account in and collision modes, the results show that collisions give the best bounds to test anomalous quartic gauge couplings with respect to and collisions. Principally, the sensitivity of the processes to anomalous couplings rapidly increases with the centerofmass energy and the luminosity.
5. Conclusions
CLIC is envisaged as a high energy 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 , , and 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 couplings with dimension8 as function of collider energies and luminosities through the processes , , and . As a result, the CLIC as photonphoton collider provides an ideal platform to examine anomalous quartic gauge couplings at high energies and luminosities.
Competing Interests
The authors declare that they have no competing interests.
References
 S. Chatrchyan, V. Khachatryan, A. M. Sirunyan 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: Publisher Site  Google Scholar
 G. Aad, T. Abajyan, B. Abbott 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: Publisher Site  Google Scholar
 G. Bélanger and F. Boudjema, “Probing quartic couplings of weak bosons through three vector production at a 500 GeV NLC,” Physics Letters B, vol. 288, no. 12, pp. 201–209, 1992. View at: Publisher Site  Google Scholar
 G. Bélanger and F. Boudjema, “${\mathrm{\gamma}\mathrm{\gamma}\to \text{W}}^{+}{\text{W}}^{}$ and $\gamma \gamma \to \text{ZZ}$ as tests of novel quartic couplings,” Physics Letters B, vol. 288, no. 12, pp. 210–220, 1992. View at: Publisher Site  Google Scholar
 M. Baak, A. Blondel, A. Bodek et al., “Study of electroweak interactions at the energy frontier,” https://arxiv.org/abs/1310.6708. View at: Google Scholar
 C. Degrande, O. Eboli, B. Feigl et al., “Monte Carlo tools for studies of nonstandard electroweak gauge boson interactions in multiboson processes: a snowmass white paper,” https://arxiv.org/abs/1309.7890. View at: Google Scholar
 O. J. P. Eboli, M. C. GonzalezGarcia, and J. K. Mizukoshi, “$pp\to {jje}^{\pm}{\mu}^{\pm}vv$ and ${jje}^{\pm}{\mu}^{\mp}vv$ at $\mathcal{O}\left({\alpha}_{em}^{6}\right)$ and $\mathcal{O}\left({\alpha}_{em}^{4}{\alpha}_{s}^{2}\right)$ for the study of the quartic electroweak gauge boson vertex at CERN LHC,” Physical Review D, vol. 74, no. 7, Article ID 073005, 2006. View at: Publisher Site  Google Scholar
 G. Abbiendi, C. Ainsley, P. F. Åkesson et al., “Constraints on anomalous quartic gauge boson couplings from $\nu \stackrel{}{\nu}\gamma \gamma $ and $q\stackrel{}{q}\gamma \gamma $ events at CERN LEP2,” Physical Review D, vol. 70, Article ID 032005, 2004. View at: Publisher Site  Google Scholar
 G. Aad, B. Abbott, J. Abdallah et al., “Measurements of $Z\gamma $ and $Z\gamma \gamma $ production in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector,” Physical Review D, vol. 93, no. 11, Article ID 112002, 41 pages, 2016. View at: Publisher Site  Google Scholar
 W. J. Stirling and A. Werthenbach, “Anomalous quartic couplings in ${W}^{+}{W}^{}\gamma $, ${Z}^{0}{Z}^{0}\gamma $ and ${Z}^{0}\gamma \gamma $ production at present and future ${e}^{+}{e}^{}$ colliders,” The European Physical Journal C—Particles and Fields, vol. 14, no. 1, pp. 103–110, 2000. View at: Publisher Site  Google Scholar
 A. GutiérrezRodríguez, C. G. Honorato, J. Montaño, and M. A. Pérez, “Limits on the quartic couplings $Z\gamma \gamma \gamma $ and $ZZ\gamma \gamma $ from ${e}^{+}{e}^{}$ colliders,” Physical Review D, vol. 89, no. 3, Article ID 034003, 2014. View at: Publisher Site  Google Scholar
 G. Belanger, F. Boudjema, Y. Kurihara, D. PerretGallix, and A. Semenov, “Bosonic quartic couplings at LEP2,” The European Physical Journal C, vol. 13, no. 2, pp. 283–293, 2000. View at: Publisher Site  Google Scholar
 G. Montagna, M. Moretti, O. Nicrosini, M. Osmo, and F. Piccinini, “Quartic anomalous couplings at LEP,” Physics Letters B, vol. 515, no. 12, pp. 197–205, 2001. View at: Publisher Site  Google Scholar
 M. Köksal, “Anomalous quartic ZZγγ couplings at the CLIC,” The European Physical Journal Plus, vol. 130, article 75, 2015. View at: Publisher Site  Google Scholar
 O. Éboli, M. GonzalézGarcía, and S. Novaes, “Quartic anomalous couplings in eγ colliders,” Nuclear Physics B, vol. 411, no. 23, pp. 381–396, 1994. View at: Publisher Site  Google Scholar
 S. Atağ and İ. Şahin, “Anomalous quartic $WW\gamma \gamma $ and $ZZ\gamma \gamma $ couplings in $e\gamma $ collision with initial beam and final state polarizations,” Physical Review D, vol. 75, no. 7, Article ID 073003, 2007. View at: Publisher Site  Google Scholar
 O. J. Éboli, M. B. Magro, P. G. Mercadante, and S. F. Novaes, “Quartic anomalous couplings in γγ colliders,” Physical Review D, vol. 52, no. 1, pp. 15–21, 1995. View at: Publisher Site  Google Scholar
 P. J. Dervan, A. Signer, W. J. Stirling, and A. Werthenbach, “Anomalous triple and quartic gauge boson couplings,” Journal of Physics G: Nuclear and Particle Physics, vol. 26, no. 5, pp. 607–615, 2000. View at: Publisher Site  Google Scholar
 O. J. P. Éboli, M. C. GonzalezGarcía, S. M. Lietti, and S. F. Novaes, “Anomalous quartic gauge boson couplings at hadron colliders,” Physical Review D, vol. 63, no. 7, Article ID 075008, 8 pages, 2001. View at: Publisher Site  Google Scholar
 E. Chapon, C. Royon, and O. Kepka, “Anomalous quartic $WW\gamma \gamma $, $ZZ\gamma \gamma $, and trilinear $WW\gamma $ couplings in twophoton processes at high luminosity at the LHC,” Physical Review D, vol. 81, no. 7, Article ID 074003, 2010. View at: Publisher Site  Google Scholar
 T. Pierzchała and K. Piotrzkowski, “Sensitivity to anomalous quartic gauge couplings in photonphoton interactions at the LHC,” Nuclear Physics B: Proceedings Supplements, vol. 179180, pp. 257–264, 2008. View at: Publisher Site  Google Scholar
 R. S. Gupta, “Probing quartic neutral gauge boson couplings using diffractive photon fusion at the LHC,” Physical Review D, vol. 85, no. 1, Article ID 014006, 2012. View at: Publisher Site  Google Scholar
 J. de Favereau de Jeneret, V. Lemaitre, Y. Liu et al., “High energy photon interactions at the LHC,” https://arxiv.org/abs/0908.2020. View at: Google Scholar
 A. Senol, “Anomalous quartic $WW\gamma \gamma $ and $ZZ\gamma \gamma $ couplings in $\gamma p$ collision at the LHC,” International Journal of Modern Physics A, vol. 29, no. 26, Article ID 1450148, 2014. View at: Publisher Site  Google Scholar
 İ. Şahin and B. Şahin, “Anomalous quartic $ZZ\gamma \gamma $ couplings in $\gamma p$ collision at the LHC,” Physical Review D, vol. 86, no. 11, Article ID 115001, 2012. View at: Publisher Site  Google Scholar
 O. J. Éboli, M. C. GonzalezGarcia, and S. M. Lietti, “Bosonic quartic couplings at CERN LHC,” Physical Review D, vol. 69, no. 9, Article ID 095005, 2004. View at: Publisher Site  Google Scholar
 H. Abramowicz, A. Abusleme, K. Afanaciev et al., “Physics at the CLIC e+e− linear collider—input to the Snowmass process 2013,” https://arxiv.org/abs/1307.5288. View at: Google Scholar
 V. I. Telnov, “Prospects of high energy photon colliders,” Nuclear and Particle Physics Proceedings, vol. 273–275, pp. 219–224, 2016. View at: Publisher Site  Google Scholar
 I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo, and V. I. Telnov, “Colliding γe and γγ beams based on singlepass ${e}^{+}{e}^{}$ accelerators II. Polarization effects, monochromatization improvement,” Nuclear Instruments and Methods in Physics Research, vol. 219, no. 1, pp. 5–24, 1984. View at: Publisher Site  Google Scholar
 S. J. Brodsky, T. Kinoshita, and H. Terazawa, “Twophoton mechanism of particle production by highenergy colliding beams,” Physical Review D, vol. 4, no. 5, pp. 1532–1557, 1971. View at: Publisher Site  Google Scholar
 H. Terazawa, “Twophoton processes for particle production at high energies,” Reviews of Modern Physics, vol. 45, no. 4, pp. 615–662, 1973. View at: Publisher Site  Google Scholar
 V. M. Budnev, I. F. Ginzburg, G. V. Meledin, and V. G. Serbo, “The twophoton particle production mechanism. Physical problems. Applications. Equivalent photon approximation,” Physics Reports, vol. 15, no. 4, pp. 181–282, 1975. View at: Publisher Site  Google Scholar
 J. M. Yang, “Probing new physics from top quark FCNC processes at linear colliders: a mini review,” Annals of Physics, vol. 316, no. 2, pp. 529–539, 2005. View at: Publisher Site  Google Scholar
 I. F. Ginzburg, “Two photon physics. Personal recollection,” https://arxiv.org/abs/1508.06581. View at: Google Scholar
 S. Atağ and A. Billur, “Possibility of determining $\tau $ lepton electromagnetic moments in $\gamma \gamma \to {\tau}^{+}{\tau}^{}$ process at the CERNLHC,” Journal of High Energy Physics, vol. 2010, article 60, 2010. View at: Publisher Site  Google Scholar
 S. Atag, S. C. Inan, and I. Sahin, “Extra dimensions in photoninduced two lepton final states at the CERN LHC,” Physical Review D, vol. 80, no. 7, Article ID 075009, 2009. View at: Publisher Site  Google Scholar
 İ. Şahin and S. C. İnan, “Probe of unparticles at the LHC in exclusive two lepton and two photon production via photonphoton fusion,” Journal of High Energy Physics, vol. 2009, no. 9, p. 69, 2009. View at: Publisher Site  Google Scholar
 S. C. Inan, “Exclusive excited leptons search in two lepton final states at the CERN LHC,” Physical Review D, vol. 81, Article ID 115002, 2010. View at: Publisher Site  Google Scholar
 I. Şahin and M. Köksal, “Search for electromagnetic properties of the neutrinos at the LHC,” Journal of High Energy Physics, vol. 2011, no. 3, article 100, 2011. View at: Publisher Site  Google Scholar
 I. Sahin and A. A. Billur, “Anomalous $WW\gamma $ couplings in $\gamma p$ collision at the LHC,” Physical Review D, vol. 83, Article ID 035011, 2011. View at: Publisher Site  Google Scholar
 M. Köksal and S. C. İnan, “Anomalous $tq\gamma $ couplings in $\gamma p$ collision at the LHC,” Advances in High Energy Physics, vol. 2014, Article ID 935840, 11 pages, 2014. View at: Publisher Site  Google Scholar
 M. Köksal and S. C. İnan, “Search for the anomalous interactions of uptype heavy quarks in $\gamma \gamma $ collision at the LHC,” Advances in High Energy Physics, vol. 2014, Article ID 315826, 8 pages, 2014. View at: Publisher Site  Google Scholar
 A. A. Billur and M. Köksal, “Probe of the electromagnetic moments of the tau lepton in γγ collisions at the CLIC,” Physical Review D, vol. 89, no. 3, Article ID 037301, 2014. View at: Publisher Site  Google Scholar
 A. Senol, “$ZZ\gamma $ and $Z\gamma \gamma $ anomalous couplings in $\gamma p$ collision at the LHC,” Physical Review D, vol. 87, Article ID 073003, 2013. View at: Publisher Site  Google Scholar
 I. Şahin, A. A. Billur, S. C. İnan et al., “Probe of extra dimensions in $\gamma q\to \gamma q$ at the LHC,” Physical Review D, vol. 88, no. 9, Article ID 095016, 8 pages, 2013. View at: Publisher Site  Google Scholar
 S. C. İnan and A. A. Billur, “Polarized top pair production in extra dimension models via photonphoton fusion at the CERN LHC,” Physical Review D, vol. 84, no. 9, Article ID 095002, 9 pages, 2011. View at: Publisher Site  Google Scholar
 İ. Şahin and B. Şahin, “Anomalous quartic $ZZ\gamma \gamma $ couplings in $\gamma p$ collision at the LHC,” Physical Review D, vol. 86, Article ID 115001, 2012. View at: Publisher Site  Google Scholar
 B. Şahin and A. A. Billur, “Anomalous $Wtb$ couplings in $\gamma p$ collision at the LHC,” Physical Review D, vol. 86, no. 7, Article ID 074026, 7 pages, 2012. View at: Publisher Site  Google Scholar
 A. A. Billur, “Anomalous topgluon couplings in $\gamma p$ collision at the CERNLHC,” Europhysics Letters, vol. 101, no. 2, Article ID 21001, 2013. View at: Publisher Site  Google Scholar
 M. Taševský, “Diffractive physics program in ATLAS experiment,” Nuclear Physics B: Proceedings Supplements, vol. 179–180, pp. 187–195, 2008. View at: Publisher Site  Google Scholar
 M. Tasevsky, “Measuring central exclusive processes at LHC,” https://arxiv.org/abs/0910.5205. View at: Google Scholar
 H. Sun, “Probe anomalous $tq\gamma $ couplings through single top photoproduction at the LHC,” Nuclear Physics B, vol. 886, pp. 691–711, 2014. View at: Publisher Site  Google Scholar
 H. Sun and C.X. Yue, “Precise photoproduction of the charged toppions at the LHC with forward detector acceptances,” The European Physical Journal C, vol. 74, no. 4, p. 2823, 2014. View at: Publisher Site  Google Scholar
 H. Sun, “Dark matter searches in jet plus missing energy events in $\gamma p$ collisions at the CERN LHC,” Physical Review D, vol. 90, no. 3, Article ID 035018, 12 pages, 2014. View at: Publisher Site  Google Scholar
 H. Sun, Y.J. Zhou, and H.S. Hou, “NLO QCD corrections to Single Top and W associated photoproduction at the LHC with forward detector acceptances,” Journal of High Energy Physics, vol. 2015, no. 2, article 064, 2015. View at: Google Scholar
 M. Köksal, “Analysis of excited neutrinos at the CLIC,” International Journal of Modern Physics A, vol. 29, no. 24, Article ID 1450138, 2014. View at: Publisher Site  Google Scholar
 M. Köksal, “Study of anomalous $WW\gamma \gamma $ coupling sensitivity at the compact linear collider,” Modern Physics Letters A, vol. 29, no. 34, Article ID 1450184, 14 pages, 2014. View at: Publisher Site  Google Scholar
 V. Arı, A. A. Billur, S. C. İnan, and M. Köksal, “Anomalous $WW\gamma $ couplings with beam polarization at the Compact Linear Collider,” Nuclear Physics B, vol. 906, pp. 211–230, 2016. View at: Publisher Site  Google Scholar
 A. GutirrezRodrguez, M. Koksal, and A. A. Billur, “Improved bounds on the dipole moments of the tau neutrino from highenergy ${\gamma}^{*}{e}^{}$ and ${\gamma}^{*}{\gamma}^{*}$ collisions at the ILC and CLIC,” Physical Review D, vol. 91, no. 9, Article ID 093008, 2015. View at: Publisher Site  Google Scholar
 S. C. İnan, “Dimensionsix anomalous $tq\gamma $ couplings in $\gamma \gamma $ collision at the LHC,” Nuclear Physics B, vol. 897, pp. 289–301, 2015. View at: Publisher Site  Google Scholar
 S. C. Inan, “Fourth generation leptons search in $\gamma \gamma \to {\mathcal{\ell}}^{}{\mathcal{\ell}}^{+}$ process at the CERNLHC,” International Journal of Modern Physics A, vol. 26, no. 21, pp. 3605–3613, 2011. View at: Publisher Site  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
 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. 2014, no. 7, article 79, 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. Diakonidis, G. J. Gounaris, and J. Layssac, “A FORTRAN code for $\gamma \gamma \to \text{Z}\text{Z}$ in SM and MSSM,” European Physical Journal, vol. 50, no. 1, pp. 47–52, 2007. View at: Publisher Site  Google Scholar
 N. Cartiglia, C. Royon, K. Akiba et al., “LHC forward physics,” Tech. Rep. CERNPHLPCC2015001, SLACPUB16364, DESY15167, 2015. View at: Google Scholar
 C. Degrande, J. L. Holzbauer, S.C. Hsu et al., “Studies of vector boson scattering and triboson production with DELPHES parametrized fast simulation for snowmass 2013,” https://arxiv.org/abs/1309.7452. View at: Google Scholar
Copyright
Copyright © 2016 M. Köksal et al. 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}.