Abstract—We study the anomalous WWJ and WWZ couplings by calculating total cross sections of two processes at the LHeC with electron beam energy Ee=140 GeV and the proton beam energy Ep=7 TeV, and at the FCC-ep collider with the polarized electron beam energy Ee=80 GeV and the proton beam energy Ep=50 TeV. At the LHeC with electron beam polarization, we obtain the results for the difference of upper and lower bounds as (0.975, 0.118) and (0.285, 0.009) for the anomalous ('NJ, OJ) and ('Nz, Oz) couplings, respectively. As for FCC-ep collider, these bounds are obtained as (1.101, 0.065) and (0.320, 0.002) at an integrated luminosity of L int =100 fb -1 . Keywords—Anomalous Couplings, Future Circular Collider, Large Hadron electron Collider, W-boson and Z-boson. I. INTRODUCTION HE SU(2)×U(1) gauge symmetry of the Standard Model (SM) results in the triple gauge boson interactions. A precise determination of the trilinear gauge boson couplings is necessary to test the validity of the SM and the presence of new physics up to a high energy scale. Since the tree-level couplings of the WWγ and WWZ vertices are fixed by the SM, any deviations from their SM values would indicate the new physics beyond the SM. The photoproduction of the W and Z bosons through triple gauge boson interactions in the lepton- hadron colliders HERA+LC and in the Large Hadron electron Collider (LHeC) has been studied theoretically in the papers [1]-[3] and [4], respectively. An investigation of the potential of the LHeC to probe anomalous WWγ coupling has been presented in [5], [6]. The present bounds on the anomalous WWγ and WWZ couplings are provided by the LEP [7], Tevatron [8], [9] and LHC [10], [11] experiments. Recently, the ATLAS [10], [11] and CMS [12], [13] Collaborations have established updated constraints on the anomalous WWγ and WWZ couplings from the γW(Z) and W + W - production processes. The results from ATLAS and I. Turk Cakir is with the Istanbul Aydin University, Applications and Research Center for Advanced Studies 34295, Sefakoy, Istanbul, Turkey (phone: +90-5333815529; fax: +90-212-4441428/22206; e-mail: ilkay.turkcakir @gmail.com). A. Senol and A. T. Tasci are with Kastamonu University, Department of Physics, 37100, Kuzeykent, Kastamonu, Turkey (e-mail: asenol@kastamonu.edu.tr, atasci@kastamonu.edu.tr). O. Cakir is with Istanbul Aydin University, Applications and Research Center for Advanced Studies 34295, Sefakoy, Istanbul, Turkey and Ankara University, Department of Physics, 06100, Tandogan, Ankara, Turkey (e- mail: ocakir@science.ankara.edu.tr). CMS experiments based on two-parameter analysis of the anomalous couplings are given in Table I. In this work, we investigate the ep→ν e qγX and ep→ν e qZX processes with anomalous WWγ and WWZ couplings at the high energy electron-proton collider LHeC and FCC-ep (Future Circular Collider-electron proton) collider [14]. LHeC is considered to be realised by accelerating electrons 140 GeV and colliding them with the 7 TeV protons. We take into account the energies of the FCC-ep as 80 GeV for electron beam and 50 TeV for proton beam. We also consider the possibility of the electron beam polarization at LHeC [15] and FCC-ep which extends the sensitivity to anomalous triple gauge boson couplings. TABLE I THE AVAILABLE 95% C.L. TWO-PARAMETER BOUNDS ON ANOMALOUS COUPLINGS ('NJ, OJ) AND (∆ΚZ, OZ) FROM THE ATLAS AND CMS EXPERIMENTS ATLAS CMS ATLAS (upper- lower) CMS (upper- lower) 'NJ -0.420,0.480 -0.250, 0.250 0.900 0.500 OJ -0.068,0.062 -0.050, 0.042 0.130 0.092 'Nz -0.045,0.045 -0.160, 0.180 0.090 0.340 Oz -0.063,0.063 -0.055, 0.055 0.126 0.110 II. ANOMALOUS COUPLINGS The WWγ and WWZ interaction vertices are described by an effective Lagrangian with the coupling constants g WWJ and g WWZ and dimensionless parameter pairs ('NJ,OJ) and ('Nz, Oz) ܮൌ  ݓݓ ఊ ሾ ଵ ఊ ൫ ఓఔ ற  ఓ ܣ ఔ െ  ఓఔ  ఓ ற ܣ ఔ ൯൅ ߢ ఊ  ఓ ற  ఔ ܣ ఓఔ ൅ ఒ ം ௠ ೈ మ  ఘఓ ற  ఔ ఓ ܣ ఔఘ ሿ൅  ݓݓ ௓ ሾ ଵ ௓ ൫ ఓఔ ற  ఓ  ఔ െ  ఓఔ  ఓ ற  ఔ ൯൅ ߢ ௓  ఓ ற  ఔ  ఓఔ ൅ ఒ ೋ ௠ ೈ మ  ఘఓ ற  ఔ ఓ  ఔఘ ሿ (1) where  ௐௐఊ ൌ  ௘ ൌ  sin ߠ ௐ and  ௐௐ௓ ൌ  cos ߠ ௐ . In general these vertices involve six C and P conserving couplings [16]. However, the electromagnetic gauge invariance requires that  ଵ ఊ ൌ 1. The anomalous couplings are defined as ߢ ௏ ൌ 1൅Δ ߢ ௏ where V=γ, Z and  ଵ ௓ ൌ 1 ൅ Δ ଵ ௓ . The W μν , Z μν and A μν are the field strength tensors for the W- boson, Z - boson and photon, respectively. The one-loop corrections to the WWγ and WWZ vertices within the framework of the SM have been studied in [17]- [19]. These corrections to the Δκ V and λ V have been found to be of the order of 10 -2 and 10 -3 , respectively. The values of the Probing Anomalous WW γ and WWZ Couplings with Polarized Electron Beam at the LHeC and FCC-Ep Collider I. Turk Cakir, A. Senol, A. T. Tasci, O. Cakir T International Science Index International Journal of Chemical, Molecular, Nuclear, Materials and Metallurgical Engineering Vol:9 No: 1, 2015 34 International Scholarly and Scientific Research & Innovation 9(1), 2015 scholar.waset.org/1999.2/10000199 International Science Index, Physical and Mathematical Sciences Vol:9, No:1, 2015 the-scholar.org/publication/10000199