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This study reported the inclusive differential production cross-section ofphotons in six pseudorapidity regions: 6.1 < $\eta$ < 6.5, 6.5 < $\eta$ < 7.0,7.0 < $\eta$ <7.5, 7.5 < $\eta$ <8.0, 8.0 < $\eta$ < 8.5, and $\eta$ > 8.5,measured through the RHICf experiment with pp collisions at $\sqrt{s}$ = 510GeV conducted in June 2017. In addition, the cross-sections in the threeregions of the $x_F$-$p_T$ phase space coverage that are same as those of theLHCf results at $\sqrt{s}$ = 7 and 13 TeV were obtained and compared.Considering the uncertainties, the results were observed to be consistent withboth the Feynman scaling law and the model predictions of EPOS-LHC,QGSJET-II-04, Sibyll 2.3d, and DPMjet-III 2019.1, although certain modelsexhibited weak collision energy dependencies.

Measurement of forward photon production cross-section in pp collisions at $\sqrt{s}$ = 510 GeV with RHICf detector