We obtain the distribution amplitude (DA) of the pion from its light-front wave functions in the basis light-front quantization framework. This light-front wave function of the pion is given by the lowest eigenvector of a light-front effective Hamiltonian consisting a three-dimensional confinement potential and the color-singlet Nambu--Jona-Lasinion interaction both between the constituent quark and antiquark. The quantum chromodynamics (QCD) evolution of the DA is subsequently given by the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution equation. Based on this DA, we then evaluate the singly and doubly virtual transition form factors in the space-like region for $pi^0rightarrow gamma^*gamma$ and $pi^0rightarrow gamma^*gamma^*$ processes using the hard-scattering formalism. Our prediction for the pion-photon transition form factor agrees well with data reported by the Belle Collaboration. However, in the large $Q^2$ region it deviates from the rapid growth reported by the BaBar Collaboration. Meanwhile, our result on the $pi^0rightarrow gamma^*gamma^*$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD.
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 present a recent calculation of the gravitational form factors (GFFs) of proton using the light-front quark-diquark model constructed by the soft-wall AdS/QCD. The four GFFs $~A(Q^2)$ , $B(Q^2)$ , $C(Q^2)$ and $bar{C}(Q^2)$ are calculated in this model. We also show the pressure and shear distributions of quarks inside the proton. The GFFs, $A(Q^2)$ and $B(Q^2)$ are found to be consistent with the lattice QCD, while the qualitative behavior of the $D$-term form factor is in agreement with the extracted data from the deeply virtual Compton scattering (DVCS) experiments at JLab, the lattice QCD, and the predictions of different phenomenological models.
We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pions gluon densities can be probed through the pion-nucleus induced $J/psi$ production data. Our pion parton distribution functions provide excellent agreement with $J/psi$ production data from widely different experimental conditions.
We construct spin-improved holographic light-front wavefunctions for the nucleons (viewed as quark-diquark systems) and use them to successfully predict their electromagnetic Sachs form factors, their electromagnetic charge radii, as well as the axial form factor, charge and radius of the proton. The confinement scale is the universal mass scale of light-front holography, previously extracted from spectroscopic data for light hadrons. With the Dirac and Pauli form factors normalized using the quark counting rules and the measured anomalous magnetic moments respectively, the masses of the quark and diquark are the only remaining adjustable parameters. We fix them using the data set for the protons Dirac-to-Pauli form factor ratio, and then predict all other data without any further adjustments of parameters. Agreement with data at low momentum-transfer is excellent. Our findings support the idea that light (pseudoscalar and vector) mesons and the nucleons share a non-perturbative universal holographic light-front wavefunction which is modified differently by their spin structures.
We investigate the leading-twist transverse momentum-dependent distribution functions (TMDs) for a physical electron, a spin-1/2 composite system consisting of a bare electron and a photon, using the Basis Light-front Quantization (BLFQ) framework. The light-front wave functions of the physical electron are obtained from the eigenvectors of the light-front QED Hamiltonian. We evaluate the TMDs using the overlaps of the light-front wave functions. The BLFQ results are found to be in excellent agreement with those TMDs calculated using lowest-order perturbation theory.
We obtain the gravitational form factors (GFFs) and investigate their applications for the description of the mechanical properties, i.e., the distributions of pressures, shear forces inside proton, and the mechanical radius, in a light-front quark-diquark model constructed by the soft-wall AdS/QCD. The GFFs, $A(Q^2)$ and $B(Q^2)$ are found to be consistent with the lattice QCD, while the qualitative behavior of the $D$-term form factor is in agreement with the extracted data from the deeply virtual Compton scattering (DVCS) experiments at JLab, the lattice QCD, and the predictions of different phenomenological models. The pressure and shear force distributions are also consistent with the results of different models.
We evaluate the cross section for the pion induced Drell-Yan process in two different models of the pion light-front wave function, inspired by light-front holographic approaches. We obtain the valence quark distribution functions in those models, which after QCD evolution, are consistent with the experimental data from the E-0615 experiment at Fermilab. Supplemented by the parton distribution functions of the target nuclei, we obtain the cross section consistent with the experimental data for the $pi^-$ Nucleus $rightarrow {mu^+mu^-X}$ Drell-Yan process.
We predict the $mathcal{V} to mathcal{P} gamma$ decay widths and the $mathcal{V} to mathcal{P} gamma^{*}$ transition form factors, where $mathcal{V}=(rho, omega, K^*, phi)$ and $mathcal{P}= (pi,K, eta,eta^prime)$, using spin-improved holographic light-front wavefunctions for the mesons. We find excellent agreement with the available data for both the decay widths and the timelike transition form factors extracted from the leptonic conversion decays $mathcal{V} to mathcal{P} l^+ l^-$.
We investigate the parton distribution functions (PDFs) of the pion and kaon from the eigenstates of a light-front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolving, are consistent with the E615 experiment at Fermilab. In addition, the ratio of the up quark distribution in the kaon to that in the pion also agrees with the NA3 experimental result at CERN.
