The HZγ coupling, which is highly sensitive to the new physics beyond the standard model, is studied through the process pp → pγp → pHX at the LHC. To this purpose, an effective Lagrangian, in a model independent approach, with dimension six operators is considered in this paper. New interaction terms regarding beyond the standard model physics include the Higgs boson anomalous vertices in both CP-even and CP-odd structures. A detailed numerical analysis is performed to scrutinize the accurate constraints on the effective HZγ couplings and to discuss how far the corresponding bounds can be improved. This is achieved by testing all the efficient Higgs decay channels and increasing the integrated luminosity at three different forward detector acceptance regions. The numerical results propose that the Higgs photoproduction at the LHC, as a complementary channel, has a great potential of exploring the HZγ couplings.The standard model (SM) remarkable predictions are currently approved to elucidate several experimental phenomena in particle physics at low energies. However, there is a variety of physical points which cannot be explained by this effective theory and this is a sensible reason to go beyond the SM (BSM) [1,2]. Although there has not been observed any direct evidence of new physics (NP) at the LHC run-I, it is anticipated to discover signals of NP at the LHC run-II with the help of new observables [3].According to the matter content of the SM and the known interaction terms, a number of frameworks are classified to probe likely NP effects at available energies. As one of the current methods, the model independent approach is extensively applicable in such studies. Here, based on the SM symmetry pattern, the conservation of lepton and baryon numbers, and the spontaneous electroweak symmetry breaking (EWSB) in the Higgs mechanism, an effective Lagrangian is formed from NP interactions between the elementary particles [4]. Indeed, integrating out heavy degrees of freedom at the BSM scale, Λ, some residual interaction terms are obtained including the gauge invariant non-renormalizable effective operators. Among these NP operators, the Higgs boson anomalous interactions are also theoretically studied in the literature [5][6][7][8][9][10][11][12][13][14][15][16][17].Following the discovery of the Higgs boson at the LHC [18][19][20], describing the properties of this particle is crucial to characterize the nature of the EWSB and to explore possible BSM physics. In the SM framework, the Higgs boson, the massless photon, and the Z boson couple indirectly via loop diagrams, containing massive charged particles. The SM prediction for the decay width of the Higgs particle in the H → Zγ channel is given bywhere, m H and m Z are the masses of the Higgs and Z boson fields, respectively [13,21]. G SM includes the W boson and top quark loops contributions and it amounts to around G SM ≃ −4.1 × 10 −5 GeV −1 . The width in Eq. (I.1) is almost equal to 6 × 10 −6 GeV, which is corresponding to a branching fraction, Br(H → Zγ) =...