Using 980 fb −1 of data at and around the ϒðnSÞ (n ¼ 1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy e þ e − collider, the two-photon process γγ → γψð2SÞ is studied from the threshold to 4.2 GeV for the first time. Two structures are seen in the invariant mass distribution of γψð2SÞ: one at M R 1 ¼ 3922.4 AE 6.5 AE 2.0 MeV=c 2 with a width of Γ R 1 ¼ 22 AE 17 AE 4 MeV, and another at M R 2 ¼ 4014.3 AE 4.0 AE 1.5 MeV=c 2 with a width of Γ R 2 ¼ 4 AE 11 AE 6 MeV; the signals are parametrized with the incoherent sum of two Breit-Wigner functions. The first structure is consistent with the Xð3915Þ or the χ c2 ð3930Þ, and the local statistical significance is determined to be 3.1σ with the systematic uncertainties included. The second matches none of the known charmonium or charmoniumlike states, and its global significance is determined to be 2.8σ including the look-elsewhere effect. The production rates are Γ γγ BðR 1 → γψð2SÞÞ ¼ 9.8 AE 3.6 AE 1.3 eV assuming ðJ PC ; jλjÞ ¼ ð0 þþ ; 0Þ or 2.0 AE 0.7 AE 0.2 eV with ð2 þþ ; 2Þ for the first structure and Γ γγ BðR 2 → γψð2SÞÞ ¼ 6.2 AE 2.2 AE 0.8 eV with ð0 þþ ; 0Þ or 1.2 AE 0.4 AE 0.2 eV with ð2 þþ ; 2Þ for the second. Here, the first errors are statistical and the second systematic, and λ is the helicity.

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