How well does nonrelativistic QCD factorization work at next-to-leading order?

Abstract

We perform a thorough investigation of the universality of the long distance matrix elements (LDMEs) of nonrelativistic QCD factorization based on a next-to-leading order (NLO) fit of $J/\ddot{I}ˆ$ color octet (CO) LDMEs to high transverse momentum $p_T$ $J/\ddot{I}ˆ$ and $\hat{I}{\cdot }_c$ production data at the LHC. We thereby apply a novel fit-and-predict procedure to systematically take into account scale variations, and predict various observables never studied in this context before. In particular, the LDMEs can well describe $J/\ddot{I}ˆ$ hadroproduction up to the highest measured values of $p_T$, as well as $\hat{I}\yen (nS)$ production via potential NRQCD based relations. Furthermore, $J/\ddot{I}ˆ$ production in ${\hat{I}}^3{\hat{I}}^3$ and ${\hat{I}}^{3}p$ collisions is surprisingly reproduced down to $p_T=1$ GeV, as long as the region of large inelasticity $z$ is excluded, which may be of significance in future quarkonium studies, in particular at the EIC and the high-luminosity LHC. In addition, our summary reveals an interesting pattern as to which observables still evade a consistent description.

6 pages, 16 figures, changes have been done to match the published version