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arXiv · 1707.03787

TMDs of Spin-one Targets: Formalism and Covariant Calculations

Yu Ninomiya·Wolfgang Bentz·Ian C. Cloët
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Abstract

We present a covariant formulation and model calculations of transverse momentum-dependent quark distribution functions (TMDs) for spin-one hadrons. Emphasis is placed on a description of these 3-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even $ρ$ meson TMDs in the framework provided by the Nambu--Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cut-off in the proper-time regularization scheme. In particular, the behavior of the 3-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Results of particular interest include the finding that the tensor polarized TMDs -- associated with spin-one hadrons -- are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator $γ^+\boldsymbolγ_Tγ_5$ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the $ρ$ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. A qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to previous experimental and theoretical results for the two-nucleon (deuteron) bound state.

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Yu Ninomiya, Wolfgang Bentz, Ian C. Cloët. 2017-10-16. TMDs of Spin-one Targets: Formalism and Covariant Calculations. https://doi.org/10.1103/physrevc.96.045206

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