Highlights from the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-factorization approach on the quarkonium production puzzles

In the framework of the ${k}_{T}$-factorization approach, we analyze the production of various quarkonium states at modern colliders and discuss the origin and the size of theoretical uncertainties. We find that the effects of the initial gluon off-shellness can provide a reasonable explanation for the $J/\ensuremath{\psi}$ spin alignment in both $\mathrm{pp}$ and $\mathrm{ep}$ collisions. We point out the fundamental role of the polarization observables, which indicate a clear difference between the collinear and noncollinear interpretations of QCD.

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