On the Rotational Invariance and Non-Invariance of Lepton Angular Distributions in Drell-Yan and Quarkonium Production

Abstract

Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be readily obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the violation of the Lam-Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred.

arXiv comment4 pages, 1 figure, revised version, to appear in Phys. Letts

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• Prospects for quarkonium studies at the high-luminosity LHC
• Rotation-invariant observables as Density Matrix invariants
• Lepton angular distributions of fixed-target Drell-Yan experiments in perturbative QCD and a geometric approach
• $J/\psi$ polarization in large-$P_T$ semi-inclusive deep-inelastic scattering at the EIC
• Lepton angular distribution of $W$ boson productions
• Glauber gluons in pion-induced Drell-Yan processes revisited