Transverse-momentum-dependent parton distribution functions up to twist 4 for spin-1 hadrons

Abstract

We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions in addition to the leading twist-2 ones by investigating all the possible decomposition of a quark correlation function in the Lorentz-invariant way. The Hermiticity and parity invariance are imposed in the decomposition; however, the time-reversal invariance is not used due to an active role of gauge links in the TMDs. Therefore, there exist time-reversal-odd functions in addition to the time-reversal even ones in the TMDs. We list all the functions up to twist-4 level because there were missing terms associated with the lightcone vector $n$ in previous works on the twist-2 part and there was no correlation-function study in the twist-3 and 4 parts for spin-1 hadrons. We show that 40 TMDs exist in the tensor-polarized spin-1 hadron in twists 2, 3, and 4. Some expressions of twist-2 structure functions are modified from previous derivations due to the new terms with $n$, and we find 30 new structure functions in twists 3 and 4 in this work. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtain new sum rules for the time-reversal-odd structure functions, $\int d^2{k}_T{h}_{LT}=\int d^2{k}_T{h}_{LL}=\int d^2{k}_T{h}_{3LL}=0$. In addition, we indicate that new transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs are rare observables to find explicit color degrees of freedom in terms of color flow, which cannot be usually measured because the color is confined in hadrons.

arXiv comment18 pages, 12 eps figures and tables, typos in abstract and summary are corrected

References in corpus (59)

• Generalized Parton Distributions
• Unraveling hadron structure with generalized parton distributions
• Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering
• Hard Exclusive Reactions and the Structure of Hadrons
• Time-reversal odd distribution functions in leptoproduction
• Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering
• The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction
• Semi-inclusive deep inelastic scattering at small transverse momentum
• Final state interactions and gauge invariant parton distributions
• Universality of T-odd effects in single spin and azimuthal asymmetries
• The Spin Structure of the Nucleon
• Transverse momentum dependence in gluon distribution and fragmentation functions
• Initial-State Interactions and Single-Spin Asymmetries in Drell-Yan Processes
• Parton Distributions in Light-Cone Gauge: Where Are the Final-State Interactions?
• Flavor Asymmetry of Antiquark Distributions in the Nucleon
• Transverse momentum dependent (TMD) parton distribution functions: status and prospects
• No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons
• Parton Fragmentation Functions
• GPD phenomenology and DVCS fitting - Entering the high-precision era
• Intrinsic transverse momentum and the polarized Drell-Yan process
• Transverse-Spin and Transverse-Momentum Effects in High-Energy Processes
• Azimuthal and Single Spin Asymmetries in Hard Scattering Processes
• Parameterization of the quark-quark correlator of a spin-1/2 hadron
• Spin Structure of the Nucleon - Status and Recent Results
• Nucleon form factors, generalized parton distributions and quark angular momentum
• Flavor Asymmetry of Light Quarks in the Nucleon Sea
• Generalized parton distributions in the deuteron
• Hadron tomography by generalized distribution amplitudes in pion-pair production process ${\gamma }^{\ast }\gamma \to {\pi }^0{\pi }^0$ and gravitational form factors for pion
• First measurement of transverse-spin-dependent azimuthal asymmetries in the Drell-Yan process
• The Spin Structure of the Nucleon
• Measurement of the transverse single-spin asymmetry in $p^{\uparrow }+p\to W^{\pm }/Z^0$ at RHIC
• Novel Phenomenology of Parton Distributions from the Drell-Yan Process
• Chiral-Odd and Spin-Dependent Quark Fragmentation Functions and their Applications
• First Measurement of the Tensor Structure Function $b_1$ of the Deuteron
• What can break the Wandzura--Wilczek relation?
• New observables in longitudinal single-spin asymmetries in semi-inclusive DIS
• Border and skewness functions from a leading order fit to DVCS data
• Lorentz invariance relations among parton distributions revisited
• Higher twist and transverse momentum dependent parton distributions: a light-front hamiltonian approach
• Generalized Parton Distributions: visions, basics, and realities
• TMDs of Spin-one Targets: Formalism and Covariant Calculations
• Lorentz invariance relations between parton distributions and the Wandzura-Wilczek approximation
• Tensor-polarized structure function $b_1$ in the standard convolution description of the deuteron
• Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons: II. parton model
• $\rho$ meson unpolarized generalized parton distributions with a light-front constituent quark model
• Transverse Spin Structure of the Nucleon
• Tensor-polarized quark and antiquark distribution functions in a spin-one hadron
• Transversity generalized parton distributions for the deuteron
• Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons: I. general formalism
• Comparison of improved TMD and CGC frameworks in forward quark dijet production
• Gravitational form factors of $\rho$ meson with a light-cone constituent quark model
• Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tagging
• Theoretical estimate on tensor-polarization asymmetry in proton-deuteron Drell-Yan process
• Enhanced Tensor Polarization in Solid-State Targets
• Gluon transversity in polarized proton-deuteron Drell-Yan process
• Deuteron polarizations in the proton-deuteron Drell-Yan process for finding the gluon transversity
• Nonperturbative-transverse-momentum effects and evolution in dihadron and direct photon-hadron angular correlations in $p$$+$$p$ collisions at $\sqrt{s}$=510 GeV
• Tensor-polarized structure functions: Tensor structure of deuteron in 2020's
• On the physics potential to study the gluon content of proton and deuteron at NICA SPD

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