$J/\psi$ production at NLO with a scale-dependent color-evaporation model

Nearly ten years ago, Kang, Ma, Qiu, and Sterman derived an evolution equation for a $Q\bar{Q}$ pair fragmenting into a quarkonium. In this study we explore the consequence of this evolution for the color-evaporation model, focusing on $J/\psi$ transverse-momentum ($p_t$) distributions in proton-proton collisions. We show that, as expected, it softens the spectrum obtained by fixed-order calculations. While next-to-leading-order calculations strongly overestimate data at large $p_t$, ours, including the (approximate) $Q\bar{Q}$ evolution and next-to-leading-order cross sections computed with Madgraph, are in good agreement with experiments. Since our study with the color-evaporation model shows a significant effect of the $Q\bar{Q}$ evolution at large $p_t$, a determination of scale-dependent long-distance-matrix elements of non-relativistic QCD could be necessary. To describe data at small and intermediate $p_t$, we use the $k_t$-factorization approach, and we argue that quarkonia data could help constrain unintegrated parton densities.