In the framework of the kT\documentclass[12pt]{minimal}
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\begin{document}$$k_T$$\end{document}-factorization approach, the production and polarization of prompt ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$\psi (2S)$$\end{document} mesons in pp collisions at LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation or, alternatively, were chosen in accordance with the Kimber–Martin–Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$\psi (2S)$$\end{document} transverse momentum distributions and then applied to describe the ATLAS and LHCb data on ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$\psi (2S)$$\end{document} production and polarization at s=7\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s} = 7$$\end{document} TeV. We perform the estimation of the polarization parameters λθ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _\theta $$\end{document}, λϕ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _\phi $$\end{document}, and λθϕ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _{\theta \phi }$$\end{document}, which determine the ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$\psi (2S)$$\end{document} spin density matrix and demonstrate that taking into account the off-shellness of the initial gluons in the color-octet contributions leads to unpolarized ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$\psi (2S)$$\end{document} production at high transverse momenta, in qualitative agreement with the LHC data.
