  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.
