Global analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization

Working in the nonrelativistic-QCD factorization framework at next-to-leading order ${\ensuremath{\alpha}}_{s}$, we fit relevant color octet long-distance matrix elements of $\ensuremath{\psi}(2S)$ meson, $⟨{\mathcal{O}}^{\ensuremath{\psi}(2S)}({^{1}S}_{0}^{[8]})⟩$, $⟨{\mathcal{O}}^{\ensuremath{\psi}(2S)}({^{3}S}_{1}^{[8]})⟩$, and $⟨{\mathcal{O}}^{\ensuremath{\psi}(2S)}({^{3}P}_{0}^{[8]})⟩$, to 1001 data points upolarized polarized inclusive hadroproduction. We do four different fits, with filters on polarization low middle transverse momentum ${p}_{T}$. find that a successful description is only possible large low-${p}_{T}$ cut. Our results are one magnitude more precise than previous determinations these elements.