Analysis of anomalous quartic $WWZ\gamma$ couplings in $\gamma p$ collision at the LHC

Gauge boson self-couplings are exactly determined by the non-Abelian gauge nature of the Standard Model (SM), thus precision measurements of these couplings at the LHC provide an important opportunity to test the gauge structure of the SM and the spontaneous symmetry breaking mechanism. It is a common way to examine the physics of anomalous quartic gauge boson couplings via effective Lagrangian method. In this work, we investigate the potential of the process $pp\rightarrow p\gamma p\rightarrow p W Z q X$ to analyze anomalous quartic $WWZ\gamma$ couplings by two different CP-violating and CP-conserving effective Lagrangians at the LHC. We calculate $95\%$ confidence level limits on the anomalous coupling parameters with various values of the integrated luminosity. Our numerical results show that the best limits obtained on the anomalous couplings $\frac{k_{0}^{W}}{\Lambda^{2}}$, $\frac{k_{c}^{W}}{\Lambda^{2}}$, $\frac{k_{2}^{m}}{\Lambda^{2}}$ and $\frac{a_{n}}{\Lambda^{2}}$ at $\sqrt{s}=14$ TeV and an integrated luminosity of $L_{int}=100$ fb$^{-1}$ are $[-1.37;\, 1.37]\times 10^{-6}$ GeV$^{-2}$, $[-1.88; \, 1.88]\times 10^{-6}$ GeV$^{-2}$, $[-6.55; \, 6.55]\times 10^{-7}$ GeV$^{-2}$ and $[-2.21;\,2.21]\times 10^{-6}$ GeV$^{-2}$, respectively. Thus, $\gamma p$ mode of photon-induced reactions at the LHC highly improves the sensitivity limits of the anomalous coupling parameters $\frac{k_{0}^{W}}{\Lambda^{2}}$, $\frac{k_{c}^{W}}{\Lambda^{2}}$, $\frac{k_{2}^{m}}{\Lambda^{2}}$ and $\frac{a_{n}}{\Lambda^{2}}$.

level limits on the anomalous coupling parameters with various values of the integrated luminosity.
Our numerical results show that the best limits obtained on the anomalous couplings respectively. Thus, γp mode of photon-induced reactions at the LHC highly improve the sensitivity limits of the anomalous coupling parameters

I. INTRODUCTION
The SM has been tested with many important experiments and it has been demonstrated to be quite successful, particularly after the discovery of a particle consistent with the Higgs boson with a mass of about 125 GeV [1,2]. Nevertheless, some of the most fundamental questions still remain unanswered. Especially, the strong CP problem, neutrino oscillations and matter -antimatter asymmetry have not been adequately clarified by the SM. It is expected to find answers to these problems of new physics beyond the SM.
where F µν is the electromagnetic field strength tensor, α is the electroweak coupling constant, a n is the strength of the parametrized anomalous quartic coupling and Λ stands for new physics scale. The anomalous W W Zγ vertex function generated by above effective Lagrangian is given in Appendix.
Second, the CP-conserving effective operators can be written by using the formalism of Ref. [4]. There are fourteen effective photonic operators with respect to the anomalous quartic gauge couplings, and they are defined by 14 independent couplings k w,b,m 0,c , k w,m 1,2,3 and k b 1,2 which are all zero in the SM. These operators can be expressed in terms of independent Also, the two independent operators for the ZZγγ interactions are parameterized as the following The five Lorentz structure belonging to W W Zγ interactions are given by with g = e/sin θ W , g z = e/sin θ W cos θ W and Here, the CP-conserving anomalous W W Zγ vertex functions generated from Eqs. (8)-(12) are given in Appendix.
Consequently, these fourteen effective photonic quartic operators can be simply expressed where For this study, we only take care of the k W i parameters (see Eqs. (18)- (20)) corresponding to the anomalous W W Zγ couplings. These k W i parameters are correlated with couplings defining anomalous W W γγ, ZZγγ and ZZZγ interactions [4]. Hence, we require to distinguish the anomalous W W Zγ couplings from the other anomalous quartic couplings. This can be accomplished to apply extra restrictions on k j i parameters as suggested by Ref. [5]. The anomalous W W Zγ couplings can be only leaved by taking k m 2 = −k m 3 while the remaining parameters are equal to zero. As a result, we express the effective interaction of W W Zγ as follows Refs. [4][5][6] are phenomenologically investigated the k m 2 Λ 2 couplings defined the anomalous quartic W W Zγ vertex. In addition, the k W 0 Λ 2 and k W c Λ 2 couplings given in Eqs. (18)- (19) constitute the present experimental limits on the anomalous quartic W W Zγ couplings within CP-conserving effective Lagrangians. Therefore, in this study, we examine limits on the CP-conserving parameters  [3,13] and γγ → W + W − Z [14,15] at linear e + e − colliders and its operating modes of eγ and γγ.
In addition, the potential of the process e + e − → e + γ * e − → e + W − Zν e [16] by making use of Equivalent Photon Approximation (EPA) at the CLIC to probe the anomalous quartic W W Zγ gauge couplings is examined. Finally, a detailed analysis of anomalous W W Zγ couplings at the LHC have been analyzed through the processes pp → W (→ jj)γZ(→ ℓ + ℓ − ) [4] and W (→ ℓν ℓ )γZ(→ ℓ + ℓ − ) [6]. Up to now, in these studies, even though the anomalous quartic W W Zγ couplings are investigated via either CP-violating or CP-conserving effective Lagrangians, they are examined by using both effective Lagrangians solely by Refs. [6,16].
The LEP provides current experimental limits on a n /Λ 2 parameter of the anomalous quartic W W Zγ couplings determined by CP-violating effective Lagrangian. Recent limits obtained through the process e + e − → W + W − γ by L3, OPAL and DELPHI collaborations are − 0.14 GeV −2 < a n Λ 2 < 0.13 GeV −2 , − 0.18 GeV −2 < a n Λ 2 < 0.14 GeV −2 (24) at 95% confidence level, respectively [17][18][19]. Nevertheless, the most stringent limits on k W 0 /Λ 2 and k W c /Λ 2 parameters described by CP-conserving effective Lagrangian are provided through the process qq ′ → W (→ ℓν)Z(→ jj)γ with an integrated luminosity of 19.3 fb −1 at √ s = 8 TeV by CMS collaboration at the LHC [7]. These are and In the coming years, since the LHC will be upgraded to center-of-mass energy of 14 TeV, it is anticipated to introduce more restrictive limits on anomalous quartic gauge boson couplings.
Photon-induced processes were comprehensively examined in ep and e + e − collisions at the HERA and LEP, respectively. In addition to pp collisions at the LHC, photon-induced processes, namely γγ and γp, enable us to test of the physics within and beyond the SM.
These processes occurring at centre-of-mass energies well beyond the electroweak scale are where m p is the mass of proton and E p is the energy of proton. dependences. Hence anomalous cross section including the W W Zγ vertex has a higher momentum dependence than the SM cross section. Therefore, γp processes are anticipated to have a high sensitivity to anomalous W W Zγ couplings since it has a higher energy reach with respect to γγ process.
However, after these processes were examined at the Tevatron, this phenomenon has led to the investigation of potential of the LHC as a γγ and γp colliders for new physics researches.
Therefore, photon-photon processes such as pp → pγγp → pe + e − p, pp → pγγp → pµ + µ − p, and pp → pγγp → pW + W − p have been analyzed from the early LHC data at √ s = 7 TeV by the CMS collaboration [30][31][32]. In addition, many studies on new physics beyond the SM through photon-induced reactions at the LHC in the literature have been phenomenologically examined. These studies contain: gauge boson self-interactions, excited neutrino, extradimensions, unparticle physics, and so forth . In this work, we have examined the CP-conserving and CP-violating anomalous quartic W W Zγ couplings through the process pp → pγp → pW Zq ′ X at the LHC.

II. THE CROSS SECTIONS AND NUMERICAL ANALYSIS
An almost real photon emitted from one proton beam can interact with the other proton and generate W and Z bosons via deep inelastic scattering in the main process pp → pγp → pW Zq ′ X. A schematic diagram defining this main process is shown in Fig. 1. The reaction γq → W Zq ′ participates as a subprocess in the main process pp → pγp → pW Zq ′ X where q = d, s,ū,c and q ′ = u, c,d,s. Corresponding tree level Feynman diagrams of the subprocess are shown in Fig. 2. As seen in Fig. 2, while only the first of these diagrams includes anomalous W W Zγ vertex, the others give SM contributions. We obtain the total cross section of pp → pγp → pW Zq ′ X process by integrating differential cross section of γq → W Zq ′ subprocess over the parton distribution functions CTEQ6L [59] and photon spectrum in EPA by using the computer package CalcHEP [60].
In Figs. 3 and 4, we plot the integrated total cross section of the process pp → pγp → pW Zq ′ X as a function of the anomalous couplings. We collect all the contributions arising from subprocesses γq → W Zq ′ while obtaining the total cross section. In addition, we presume that only one of the anomalous quartic gauge couplings is non zero at any given time, while the other couplings are fixed to zero. We can see from Fig. 3 that deviation from SM value of the anomalous cross section containing the coupling k m 2 Λ 2 is larger than For this reason, the limits obtained on the coupling k m 2 Λ 2 from analysed process are anticipated to be more restrictive than the limits on We calculate the sensitivity of the process pp → pγp → pW Zq ′ X to anomalous quartic gauge couplings by applying one and two-dimensional χ 2 criterion without a systematic error. The χ 2 function is defined as follows where σ N P is the cross section in the existence of new physics effects, δ stat = 1 √ N is the statistical error: N is the number of events. The number of expected events of the process where L int denotes the integrated luminosity, σ SM is the SM cross section and ℓ = e − or µ − . We impose both cuts for transverse momentum of final state quarks to be p j T > 15 GeV and the pseudorapidity of final state quarks to be |η| < 2.5 since ATLAS and CMS have central detectors with a pseudorapidity coverage |η| < 2.5. The minimal transverse momentum cut of an outgoing proton is taken to be p T > 0.1 GeV within the photon spectrum.
In Tables I-III, we give the one-dimensional limits on anomalous quartic gauge couplings

III. CONCLUSIONS
The LHC with forward detector equipment is a suitable platform to examine physics within and beyond the SM via γγ and γp processes. γp process has the high luminosities and high center-of-mass energies compared to γγ process. Moreover, γp process due to the remnants of only one of the proton beams provides rather clean experimental conditions according to pure deep inelastic scattering of pp process. For these reasons, we examine the process pp → pγp → pW ZqX in order to determine anomalous quartic W W Zγ parameters k m 2 Λ 2 and an Λ 2 obtained by using two different CP-violating and CP-conserving effective Lagrangians at the LHC. A featured advantage of the process pp → pγp → pW ZqX is that it isolates anomalous W W Zγ couplings. It enables us to probe W W Zγ couplings independent of W W γγ. Our limits on k W 0 Λ 2 and k W c Λ 2 are approximately one order better than the LHC's limits [7] while the limits obtained on an Λ 2 can set more stringent limit by five orders of magnitude compared to LEP results [17]. Moreover, we compare our limits with phenomenological studies on the anomalous k m 2 Λ 2 and an Λ 2 couplings at the LHC and CLIC. Ref. [16] have considered semi-leptonic decay channel of the final W and Z bosons in the cross section calculations to improve the limits on anomalous an Λ 2 and k m 2 Λ 2 couplings at the CLIC. We can see that the limits on anomalous an Λ 2 and k m 2 Λ 2 couplings expected to be obtained with L int = 590 fb −1 and √ s = 3 TeV are almost 2 times better than our best limits.