TMDs of Spin-one Targets: Formalism and Covariant Calculations

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 $\rho$ 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 ${\gamma }^{+}{\mathbf{\gamma }}_T{\gamma }_5$ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the $\rho$ 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.

16 pages, 9 figures (updated to agree with journal version -- some changes in notation)

References in corpus (7)

• Parton Fragmentation Functions
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• Role of diquark correlations and the pion cloud in nucleon elastic form factors
• Transversity quark distributions in a covariant quark-diquark model
• Light Meson Form Factors at near Physical Masses
• The NJL-jet model for quark fragmentation functions
• Dressed Quark Mass Dependence of Pion and Kaon Form Factors

Cited by in corpus (22)

• Parton Distribution Functions of Heavy Mesons on the Light Front
• Transverse-momentum-dependent parton distribution functions up to twist 4 for spin-1 hadrons
• Basis light-front quantization approach to photon
• Light-front holographic $\rho$-meson distributions in the momentum space
• Light-front wavefunctions of mesons by design
• Leading twist T-even TMDs for the spin-1 heavy vector mesons
• Gluon and valence quark distributions for the pion and kaon in nuclear matter
• Transverse momentum distributions of valence quark in light and heavy vector mesons
• Nuclear medium meson structures from the Schwinger proper-time Nambu--Jona-Lasinio model
• Inclusive and semi-inclusive production of spin-3/2 hadrons in $e^{+}{e}^{-}$ annihilation
• Experimental Study of Tensor Structure Function of Deuteron
• Intrinsic Glue and Wilson lines within Dressed Quarks
• Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Semi-inclusive deep inelastic scattering off a tensor-polarized spin-1 target
• Valence quark distribution of light $\rho$ and heavy $J/\psi$ vector mesons in light-cone quark model
• Medium effects on the electromagnetic form factors of the $\rho$ meson
• Parton Distribution Functions for Pseudoscalar Mesons in the COnfining Effective Chiral Quark Theory
• The kaon off-shell generalized parton distributions and transverse momentum dependent parton distributions
• Novel relations for twist-3 tensor-polarized fragmentation functions in spin-1 hadrons
• Impact of Charge Symmetry Breaking on Gluon and Sea Quark Distributions in the Pion and Kaon
• Twist-3 contribution in the Drell-Yan process with tensor-polarized deuteron
• Pion generalized parton distributions at zero skewness