Advances in High Energy Physics

Volume 2016 (2016), Article ID 8672391, 8 pages

http://dx.doi.org/10.1155/2016/8672391

## Search for Anomalous Quartic Couplings in Photon-Photon Collisions

^{1}Department of Optical Engineering, Cumhuriyet University, 58140 Sivas, Turkey^{2}Department of Physics, Ankara University, 06100 Ankara, Turkey^{3}Department of Physics, Abant Izzet Baysal University, 14280 Bolu, Turkey

Received 16 June 2016; Revised 23 September 2016; Accepted 18 October 2016

Academic Editor: Edward Sarkisyan-Grinbaum

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}.

#### 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 processes , , and to examine the anomalous quartic couplings of vertex at the Compact Linear Collider (CLIC) with center-of-mass energy 3 TeV. We calculate confidence level sensitivities on the dimension-8 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 center-of-mass 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 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 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 symmetry and local symmetry, dimension-6 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 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 () 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 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 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 dimensions-6 analogue.

The experimental 95% CL bounds on dimension-6 couplings at the LEP by OPAL collaboration through the process are [8]

The 95% CL one-dimensional bounds on dimension-8 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 Monte-Carlo 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 center-of-mass 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 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 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, quasi-real 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 quasi-real flux in and 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 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 photon-induced 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 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].