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Light-Front Transverse Momentum Distributions for ${\cal J}$=1/2 Hadronic Systems in Valence Approximation
Nuclear Theory · Submitted 21 Jul 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The light-front spin-dependent spectral function is fully determined by six scalar functions that allow for a complete description of the six T-even transverse-momentum distributions, suitable for a detailed investigation of the dynamics inside the bound system.
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The abstract, sentence by sentence
The semi-inclusive correlator for a ${\cal J}$=1/2 bound-system, composed by A spin-1/2 fermions, is linearly expressed in terms of the light-front Poincar\'e covariant spin-dependent spectral function, in valence approximation. The light-front spin-dependent spectral function is fully determined by six scalar functions that allow for a complete description of the six T-even transverse-momentum distributions, suitable for a detailed investigation of the dynamics inside the bound system. The application of the developed formalism to a case with a sophisticated dynamical content, like $^3$He, reaches two goals: (i) to illustrate a prototype of an investigation path for gathering a rich wealth of information on the dynamics and also finding valuable constraints to be exploited from the phenomenological standpoint; (ii) to support for the three-nucleon system a dedicated experimental effort for obtaining a detailed 3D picture in momentum space. In particular, the orbital-angular momentum decomposition of the bound state can be studied through the assessment of relations among the transverse-momentum distributions, as well as the relevance of the relativistic effect generated by the implementation of macrocausality. A fresh evaluation of the longitudinal and transverse polarizations of the neutron and proton is also provided, confirming essentially the values used in the standard procedure for extracting the neutron structure functions from both deep-inelastic scattering and semi-inclusive reactions, in the same kinematical regime.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The semi-inclusive correlator for a ${\cal J}$=1/2 bound-system, composed by A spin-1/2 fermions, is linearly expressed in terms of the light-front Poincar\'e covariant spin-dependent spectral function, in valence approximation. | contribution 0.64 | 0.80 | 0.29 | asserted 1.00 |
| s1 | The light-front spin-dependent spectral function is fully determined by six scalar functions that allow for a complete description of the six T-even transverse-momentum distributions, suitable for a detailed investigation of the dynamics inside the bound system. | contribution 0.44 | 0.78 | 0.36 | asserted 1.00 |
| s2 | The application of the developed formalism to a case with a sophisticated dynamical content, like $^3$He, reaches two goals: (i) to illustrate a prototype of an investigation path for gathering a rich wealth of information on the dynamics and also finding valuable constraints to be exploited from the phenomenological standpoint; (ii) to support for the three-nucleon system a dedicated experimental effort for obtaining a detailed 3D picture in momentum space. | contribution 0.67 | 0.83 | 0.33 | asserted 0.98 |
| s3 | In particular, the orbital-angular momentum decomposition of the bound state can be studied through the assessment of relations among the transverse-momentum distributions, as well as the relevance of the relativistic effect generated by the implementation of macrocausality. | contribution 0.54 | 0.55 | 0.09 | asserted 0.68 |
| s4 | A fresh evaluation of the longitudinal and transverse polarizations of the neutron and proton is also provided, confirming essentially the values used in the standard procedure for extracting the neutron structure functions from both deep-inelastic scattering and semi-inclusive reactions, in the same kinematical regime. | result 0.97 | 0.86 | 0.12 | asserted 0.98 |
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The paper
Original abstract
The semi-inclusive correlator for a ${\cal J}$=1/2 bound-system, composed by A spin-1/2 fermions, is linearly expressed in terms of the light-front Poincar\'e covariant spin-dependent spectral function, in valence approximation. The light-front spin-dependent spectral function is fully determined by six scalar functions that allow for a complete description of the six T-even transverse-momentum distributions, suitable for a detailed investigation of the dynamics inside the bound system. The application of the developed formalism to a case with a sophisticated dynamical content, like $^3$He, reaches two goals: (i) to illustrate a prototype of an investigation path for gathering a rich wealth of information on the dynamics and also finding valuable constraints to be exploited from the phenomenological standpoint; (ii) to support for the three-nucleon system a dedicated experimental effort for obtaining a detailed 3D picture in momentum space. In particular, the orbital-angular momentum decomposition of the bound state can be studied through the assessment of relations among the transverse-momentum distributions, as well as the relevance of the relativistic effect generated by the implementation of macrocausality. A fresh evaluation of the longitudinal and transverse polarizations of the neutron and proton is also provided, confirming essentially the values used in the standard procedure for extracting the neutron structure functions from both deep-inelastic scattering and semi-inclusive reactions, in the same kinematical regime.
Human review
References
How the literature uses it
5 arXiv papers cite this in 22 sentences
Papers citing it · 18 sentences without a confident label
Uses its method or tool 1 paper
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For $A=3$, Eq. (4), in terms of the wf in momentum space, $G_L_ρX^j_23 l_23s_23(k_23,k)$, reads [ref] n^N(ξ, k_⊥) = ∑_T_23,τ_23 ⟨T_23 τ_23 1 2 τ|1 2 T_z ⟩^2 ∫_0^∞d k_23 k^2_23 ×E_23 E(k) 4 π (1- ξ) k^+ ∑_j_23,l_23,s_23 ∑_L_ρ,X | G_L_ρX^j_23 l_23s_23(k_23,k)|^2 ,
The European Muon Collaboration effect in Light-Front Hamiltonian Dynamics · Introduction · 0.81
Uses its data or values 1 paper
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Since the light-cone distributions entering Eq. (9) of the main text are numerically evaluated from the TMDs of Ref. [ref] , from a numerical point of view, the nuclear SSF cannot be evaluated at $x=0$.
$^3$He spin-dependent structure functions within the relativistic Light-Front Hamiltonian dynamics · S4: Test of the Bjorken sum rule · 0.89
Cites it as support 1 paper
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It is worth noticing that, in our Poincaré-covariant framework, the momentum distribution fulfills both normalization (i.e. the baryon number sum rule) and momentum sum rule [ref] .
The European Muon Collaboration effect in Light-Front Hamiltonian Dynamics · Introduction · 0.96
Cites it as background 1 paper
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where $Δf^N(ξ, k_⊥)$ and $Δ_T' f^N(ξ, k_⊥)$ are two out of the six leading-twist transverse-momentum distributions [ref] .
The European Muon Collaboration effect in Light-Front Hamiltonian Dynamics · Introduction · 0.86
What it cites · 64 sentences without a confident label
Contests 3 papers
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The other relation proposed in Refs. [ref] , between the TMDs, a quadratic one, does not hold in any case, since the TMDs are given by integrals over the relative momentum of the spectator interacting pair,
Modelling quark distribution and fragmentation functions · Conclusions · contest 0.85
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The other relation proposed in Refs. [ref] , between the TMDs, a quadratic one, does not hold in any case, since the TMDs are given by integrals over the relative momentum of the spectator interacting pair,
On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions · Conclusions · contest 0.85
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Therefore one cannot anymore use the parametrization with only three scalar functions considered in Ref. [ref] .
Investigation of the Neutron Form Factors by Inclusive Quasi-Elastic Scattering of Polarized Electrons off Polarized $^{3}$He: A Theoretical Overview · The LF spin-dependent spectral function and the LF spin-dependent momentum distribution · contest 0.71
Uses the method or tool of 3 papers
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from the three-body wave function, using Eq. ([ref]) and the expression for the LF spin-dependent spectral function given by Eq. (72) of Ref. [ref] .
Light-Front spin-dependent Spectral Function and Nucleon Momentum Distributions for a Three-Body System · The LF spin-dependent spectral function and the LF spin-dependent momentum distribution · 0.93
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The traces of $Φ_V$ in Eqs. ([ref],[ref],[ref]), i. e. the traces needed when the correlator is expanded at twist-two level considering only the T-even terms, can be expressed by traces of the spectral function with the help of Eq. ([ref]) and of the following equalities for the matrix elements of $γ$ matrixes between LF spinors (see Ref. [ref] )
Poincare' Covariant Current Operator and Elastic Electron-Deuteron Scattering in the Front-form Hamiltonian Dynamics · Traces of the Valence Correlator and of the light-front Spectral Function · 0.90
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In the last step the first of the bipolar harmonics in Eq. (A5) of Ref. [ref] has been used.
Investigation of the Neutron Form Factors by Inclusive Quasi-Elastic Scattering of Polarized Electrons off Polarized $^{3}$He: A Theoretical Overview · Spin-dependent momentum distribution · 0.95
Compares with 2 papers
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Moreover we have assessed the approximated relations relations between the TMDs, investigated in Refs. [ref] with the aim to offer a guide for the extraction of TMDs from experimental data.
On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions · Introduction · 0.80
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Moreover we have assessed the approximated relations relations between the TMDs, investigated in Refs. [ref] with the aim to offer a guide for the extraction of TMDs from experimental data.
Modelling quark distribution and fragmentation functions · Introduction · 0.80
Cites as background 29 papers
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with $p̃=(p^+,p_⊥)$ the LF particle momentum in the lab frame and $u(p̃,σ)$, $v(p̃,σ)$ the particle and anti-particle LF spinors [ref] .
Quantum Chromodynamics and Other Field Theories on the Light Cone · The Semi-Inclusive Correlator for a $J=1/2$ bound system and the LF spectral function · 0.80
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with $p̃=(p^+,p_⊥)$ the LF particle momentum in the lab frame and $u(p̃,σ)$, $v(p̃,σ)$ the particle and anti-particle LF spinors [ref] .
Poincare' Covariant Current Operator and Elastic Electron-Deuteron Scattering in the Front-form Hamiltonian Dynamics · The Semi-Inclusive Correlator for a $J=1/2$ bound system and the LF spectral function · 0.80
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In particular light-cone models and phenomenological approaches for the TMDs have been used, e.g., (i) to study the three-dimensional nucleon structure [ref] ,
On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions · Introduction · 0.85
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