The first study of J/ψϕ production in diffractive processes in proton-proton collisions is presented. The study is based on an LHCb dataset recorded at center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5 fb^{-1}. The data disfavor a nonresonant J/ψϕ production but are consistent with a resonant model including several resonant states observed previously only in B^{+}→J/ψϕK^{+} decays. The χ_{c0}(4500) state is observed with a significance over 6σ and the χ_{c1}(4274) is confirmed with a significance of more than 4σ.
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