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Register a new userForces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case
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We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. It is important that the transformation ensures 2D stability conditions if the 3D stability conditions are satisfied. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large $N_c$ nucleon as a chiral soliton.
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We investigate the two-dimensional energy-momentum-tensor (EMT) distributions of the nucleon on the light front, using the Abel transforms of the three-dimensional EMT ones. We explicitly show that the main features of all EMT distributions are kept intact in the course of the Abel transform. We also examine the equivalence between the global and local conditions for the nucleon stability in the three-dimensional Breit frame and in the two-dimensional transverse plane on the light front. We also discuss the two-dimensional force fields inside a nucleon on the light front.
In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.
We investigate the two-dimensional transverse charge distributions of the transversely polarized nucleon. As the longitudinal momentum ($P_z$) of the nucleon increases, the electric dipole moment is induced, which causes the displacement of the transverse charge and magnetization distributions of the nucleon. The induced dipole moment of the proton reaches its maximum value at around $P_z approx 3.2$ GeV due to the kinematical reason. We also investigate how the Abel transformations map the three-dimensional charge and magnetization distributions in the Breit frame on to the transverse charge and magnetization ones in the infinite momentum frame.
We produce the light-front wave functions (LFWFs) of the nucleon from a basis light-front ap- proach in the leading Fock sector representation. We solve for the mass eigenstates from a light-front effective Hamiltonian, which includes a confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with fixed coupling. We then employ the LFWFs to obtain the electromagnetic and axial form factors, the par- ton distribution functions (PDFs) and the generalized parton distribution functions for the nucleon. The electromagnetic and axial form factors of the proton agree with the experimental data, whereas the neutron form factors deviate somewhat from the experiments in the low momentum transfer region. The unpolarized, the helicity, and the transversity valence quark PDFs, after QCD scale evolution, are fairly consistent with the global fits to the data at the relevant experimental scales. The helicity asymmetry for the down quark also agrees well with the measurements, however, the asymmetry for the up quark shows a deviation from the data, especially in the small x region. We also find that the tensor charge agrees well with the extracted data and the lattice QCD predictions, while the axial charge is somewhat outside the experimental error bar. The electromagnetic radii of the proton, the magnetic radius of the neutron, and the axial radius are in excellent agreement with the measurements, while the neutron charge radius deviates from experiment.
We calculate the cross section of the electron scattering from a bound nucleon within light-front approximation. The advantage of this approximation is the possibility of systematic account for the off-shell effects which become essential in high energy electro-nuclear processes aimed at probing the nuclear structure at small distances. We derive a new dynamical parameter which allows to control the extent of the off-shellness of electron - bound-nucleon electromagnetic current for different regions of momentum transfer and initial light-cone momenta of the bound nucleon. The derived cross section is compared with the results of other approaches in treating the off-shell effects in electron-nucleon scattering.
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