Measurements of Angular Distributions of Muons From Upsilon Meson Decays in p p-bar Collisions at sqrt(s)=1.96 TeV

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Rotational invariance of λ ~ \tilde{\lambda} follows from the invariance of the expression ∑ n = − J J ( − 1 ) n ⟨ ψ | n ⟩ ⟨ − n | ψ ⟩ \sum_{n=-J}^{J}(-1)^{n}\langle\psi|n\rangle\langle-n|\psi\rangle , in which | ψ ⟩ |\psi\rangle is a general state vector for a particle of spin J J and | n ⟩ |n\rangle are the standard J z J_{z} basis eigenstates
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See Supplemental Material at [URL will be inserted by publisher] for complete tables of results for λ θ \lambda_{\theta} , λ φ \lambda_{\varphi} , λ θ φ \lambda_{\theta\varphi} and λ ~ \tilde{\lambda} in both the s s –channel helicity frame and Collins–Soper frame for the Υ ⁡ ( 1 S ) \Upsilon(1S) , Υ ⁡ ( 2 S ) \Upsilon(2S) , and Υ ⁡ ( 3 S ) \Upsilon(3S)
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