Global analysis of $\psi (2S)$ inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization

Working in the nonrelativistic-QCD factorization framework at next-to-leading order in ${\alpha }_s$, we fit the relevant color octet (CO) long-distance matrix elements (LDMEs) of the $\psi (2S)$ meson, $⟨{\mathcal{O}}^{\psi (2S)}({{}^{1}S}_0^{[8]})⟩$, $⟨{\mathcal{O}}^{\psi (2S)}({{}^{3}S}_1^{[8]})⟩$, and $⟨{\mathcal{O}}^{\psi (2S)}({{}^{3}P}_0^{[8]})⟩$, to 1001 data points of upolarized and polarized $\psi (2S)$ inclusive hadroproduction. We do four different fits, with filters on polarization and low to middle transverse momentum $p_T$. We find that a successful description of the data is only possible with a large low-$p_T$ cut. Our results are one order of magnitude more precise than previous determinations of these color octet long-distance matrix elements.