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, $\langle {\cal O}^{\psi(2S)}({^1S}_0^{[8]})\rangle$, $\langle {\cal O}^{\psi(2S)}({^3S}_1^{[8]})\rangle$, and $\langle {\cal O}^{\psi(2S)}({^3P}_0^{[8]})\rangle$, 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.