Curing the high-energy perturbative instability of vector-quarkonium-photoproduction cross sections at order $$\alpha \alpha _s^3$$ with high-energy factorisation

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Abstract We cure the perturbative instability of the total-inclusive-photoproduction cross sections of vector S-wave quarkonia observed at high photon-proton-collision energies ( $$\sqrt{s_{\gamma p}}$$ s γ p ) in Next-to-Leading Order (NLO) Collinear-Factorisation (CF) computations. This is achieved using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA), which is a subset of the Leading-Logarithmic Approximation (LLA) of HEF which resums higher-order QCD corrections proportional to $$\alpha _s^n \ln ^{n-1} ({\hat{s}}{/}M^2)$$ α s n ln n - 1 ( s ^ / M 2 ) in the Regge limit $${\hat{s}}\gg M^2$$ s ^ ≫ M 2 with $$M^2$$ M 2 being the quarkonium mass and $${\hat{s}}$$ s ^ is the squared partonic-center-of-mass energy. Such a DLA is strictly consistent with the NLO and NNLO DGLAP evolutions of the parton distribution functions. By improving the treatment of the large- $${\hat{s}}$$ s ^ asymptotics of the CF coefficient function, the resummation cures the unphysical results of the NLO CF calculation. The matching is directly performed in $${\hat{s}}$$ s ^ space using the Inverse-Error Weighting matching procedure which avoids any possible double counting. The obtained cross sections are in good agreement with data. In addition, the scale-variation uncertainty of the matched result is significantly reduced compared to the LO results. Our calculations also yield closed-form analytic limits for $${\hat{s}}\gg M^2$$ s ^ ≫ M 2 of the NLO partonic CF and numerical limits for contributions to those at NNLO scaling like $$\alpha _s^2 \ln ({\hat{s}}/M^2)$$ α s 2 ln ( s ^ / M 2 ) .

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