Quarkonium polarization in pp and p-nucleus collisions Pietro Faccioli a , Carlos Lourenc ¸o b , Jo˜ ao Seixas a,c , Hermine K. W ¨ ohri a a Laborat´ orio de Instrumenta¸ c˜ ao e F´ ısica Experimental de Part´ ıculas (LIP), Lisbon, Portugal b European Organization for Nuclear Research (CERN), Geneva, Switzerland c Physics Department, Instituto Superior T´ ecnico (IST), Lisbon, Portugal Abstract The existing measurements of quarkonium polarization in proton-antiproton and proton-nucleus collisions are puz- zling. We highlight issues which are often underestimated in the experimental analyses: the importance of the choice of the reference frame, the interplay between observed decay and production kinematics, and the consequent influence of the experimental acceptance on the comparison between experimental measurements and theoretical calculations. New measurements must provide more detailed information, such that physical conclusions can be derived without relying on model-dependent assumptions. We also describe a frame-invariant formalism which minimizes the depen- dence of the measurements on the experimental acceptance, facilitates the comparison with theoretical calculations, and probes systematic effects due to experimental biases. Keywords: Quarkonium, polarization, QCD 1. The experimental situation Detailed studies of quarkonium production should provide significant progress in our understanding of quantum chromodynamics (QCD) [1]. However, our present understanding of this physics topic is rather limited, despite the multitude of experimental data accumulated over more than 30 years. The p T differential J/ψ and ψ ′ direct production cross sections measured (in the mid 1990’s) by CDF, in p¯ p collisions at 1.8 TeV [2], were seen to be around 50 times larger than the available expectations, based on leading order calculations made in the scope of the Colour Singlet Model. The non-relativistic QCD (NRQCD) framework [3], where quarkonia can also be produced as coloured quark pairs, succeeded in describing the measurements, opening a new chapter in the studies of quarkonium production physics. However, these calculations depend on non-perturbative parameters, the long distance colour octet matrix elements, which have been freely adjusted to the data, thereby decreasing the impact of the resulting agreement between data and calculations. More recently, calculations of next-to-leading-order (NLO) QCD corrections to colour- singlet quarkonium production showed an important increase of the high- p T rate, significantly decreasing the colour- octet component needed to reproduce the quarkonium production cross sections measured at the Tevatron [4]. Given this situation, differential cross sections are clearly insufficient information to ensure further progress in our understanding of quarkonium production. Studies of the polarization of the J PC = 1 -- quarkonium states, which decay into lepton pairs, will certainly provide very useful complementary information. In fact, the competing mecha- nisms dominating in the different theoretical approaches lead to very different expected polarizations of the produced quarkonia. On one hand, the NRQCD calculations [5, 6, 7], dominated by the colour-octet component, predict that, at Tevatron or LHC energies and at asymptotically high p T , the directly produced ψ ′ and J/ψ mesons are produced almost fully transversely polarized (i.e. with dominant angular momentum component J z = ±1) with respect to their own Nuclear Physics A 855 (2011) 116–124 0375-9474/$ – see front matter © 2011 Elsevier B.V. All rights reserved. www.elsevier.com/locate/nuclphysa doi:10.1016/j.nuclphysa.2011.02.027