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Abstract In this paper, potential of the LHC to explore the phenomenology of the Randall–Sundrum-like scenario with the small curvature for the process $$pp \rightarrow p \gamma \gamma p \rightarrow p \mu ^- \mu ^+p $$ pp→pγγp→pμ-μ+p through the subprocess $$\gamma \gamma \rightarrow \mu ^- \mu ^+$$ γγ→μ-μ+ is examined for two forward detector acceptances, $$0.0015< \xi < 0.5$$ 0.0015<ξ<0.5 and $$0.1< \xi <0.5$$ 0.1<ξ<0.5 . This process is known to be one of the most clean channels. The sensitivity bounds on the anomalous model parameters have been found at the $$95\%$$ 95% confidence level for various LHC integrated luminosity values.