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$ψ(2S)$ and $Υ(3S)$ hadroproduction in the parton Reggeization approach: Yield, polarization, and the role of fragmentation

The hadroproduction of the radially excited heavy-quarkonium states $ψ(2S)$ and $Υ(3S)$ at high energies is studied in the parton reggeization approach and the factorization formalism of nonrelativistic QCD at lowest order in the strong-coupling constant $α_s$ and the relative heavy-quark velocity $v$. A satisfactory description of the $ψ(2S)$ transverse-momentum ($p_T$) distributions measured by ATLAS, CMS, and LHCb at center-of-mass energy $\sqrt{S}=7$ TeV is obtained using the color-octet long-distance matrix elements (LDMEs) extracted from CDF data at $\sqrt{S}=1.96$ TeV. The importance of the fragmentation mechanism and the scale evolution of the fragmentation functions in the upper $p_T$ range, beyond 30 GeV, is demonstrated. The $Υ(3S)$ $p_T$ distributions measured by CDF at $\sqrt{S}=1.8$ TeV and by LHCb at $\sqrt{S}=7$ TeV and forward rapidities are well described using LDMEs fitted to ATLAS data at $\sqrt{S}=7$ TeV. Comparisons of polarization measurements by CDF and CMS at large $p_T$ values with our predictions consolidate the familiar problem in the $ψ(2S)$ case, but yield reasonable agreement in the $Υ(3S)$ case.