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We revisit inclusive J/psi and Upsilon photoproduction at lepton-hadroncolliders, namely in the limit when the exchanged photon is quasi real. Ourcomputation includes the next-to-leading-order (NLO) alpha_s corrections to theleading-order contributions in v. Similarly to the case of NLOcharmonium-hadroproduction processes, the resulting cross sections obtained inthe MS-bar factorisation scheme are sometimes found to be negative. We showthat the scale-fixing criteria which we derived in a previous study of eta(c)production successfully solves this problem from the EicC all the way up to theFCC-eh energies. We then elaborate on how to study a scale uncertainty akin tothat derived by scale variations when one fixes a scale. In turn, weinvestigate where both J/psi and Upsilon photoproduction could be used toimprove our knowledge of gluon content of the proton at scales as low as acouple of GeV.

Revisiting NLO QCD corrections to total inclusive J/psi and Upsilon photoproduction cross sections in lepton-proton collisions