Basis Light-front Quantization Research Articles

Generalized parton distributions and spin structures of light mesons from a light-front Hamiltonian approach

We present the generalized parton distributions (GPDs) for the valence quarks of the pion and the kaon in both momentum space and position space within the basis light-front quantization framework. These GPDs are obtained from the eigenvectors of a light-front effective Hamiltonian consisting of the holographic quantum chromodynamics (QCD) confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu-Jona--Lasinio interactions for the valence quarks of mesons. We then calculate the generalized form factors of the pion and the kaon from the moments of these GPDs. Combining the tensor form factors with the electromagnetic form factors, we subsequently evaluate the impact parameter dependent probability density of transversely polarized quarks inside the pion and the kaon. The numerical results for the generalized form factors, corresponding charges, as well as those for the probability densities and the transverse shift of the polarized densities are consistent with lattice QCD simulations and with chiral quark models.

Nucleon structure from basis light-front quantization

We produce the light-front wave functions (LFWFs) of the nucleon from a basis light-front approach 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 parton 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 protons, the magnetic radius of the neutron, and the axial radius are in excellent agreement with the measurements, while the neutron charge radius deviates from the experiment.

Pion to photon transition form factors with basis light-front quantization

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 $\pi^0\rightarrow \gamma^*\gamma$ and $\pi^0\rightarrow \gamma^*\gamma^*$ 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 $\pi^0\rightarrow \gamma^*\gamma^*$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD.

Semileptonic decay of Bc to ηc and J/ψ on the light front

We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $\eta_c$ or $J/\psi$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $\eta_c'$ and the $\psi'$. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of current component, we propose a preferred set of frames to calculate these form factors.

Simulating hadronic physics on noisy intermediate-scale quantum devices using basis light-front quantization

The analogy between quantum chemistry and light-front quantum field theory, first noted by Wilson, serves as motivation to develop light-front quantum simulation of quantum field theory. We demonstrate how calculations of hadron structure can be performed on noisy intermediate-scale quantum devices within the basis light-front quantization (BLFQ) framework. Within BLFQ, relativistic quantum field theories take a form that permits direct application of methods for digital quantum simulation of quantum chemistry, which can be readily scaled into the quantum advantage regime. We calculate the light-front wave functions of pions using an effective light-front Hamiltonian in a basis representation on a current quantum processor. We use the variational quantum eigensolver to find the ground-state energy and the corresponding wave function, which is subsequently used to calculate pion mass radius, decay constant, elastic form factor, and charge radius.

Light-Front Field Theory on Current Quantum Computers.

We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.

Transverse structure of electron in momentum space in basis light-front quantization

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.

Light mesons within the basis light-front quantization framework

We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Based on these LFWFs, we then study the structure of these mesons by computing the electromagnetic form factors, the decay constants, the parton distribution amplitudes (PDAs), and the parton distribution functions (PDFs). Our results are comparable to those from experiments and other theoretical models.

Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

The framework of 'time-dependent basis light-front quantisation' (tBLFQ) offers a non-perturbative approach to scattering problems in external fields, based on Fock space truncation. Here we extend tBLFQ to include spatio-temporal field inhomogeneities in multiple spacetime directions. This extension is necessary for the proper modelling of e.g. intense laser fields. We focus on the example of nonlinear Compton scattering of an electron on an axicon-type laser, with an emphasis on the transverse structure of the beam. We analyse the impact of field intensity and particle energy, as well as basis truncation effects, on the radiation spectrum of the scattered electron.

Parton distribution functions of heavy mesons on the light front

The parton distribution functions (PDFs) of heavy mesons are evaluated from their light-front wave functions, which are obtained from a basis light-front quantization in the leading Fock sector representation. We consider the mass eigenstates from an effective Hamiltonian consisting of the confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with running coupling. We present the gluon and the sea quark PDFs which we generate dynamically from the QCD evolution of the valence quark distributions.

Heavy-light mesons on the light front

We study the heavy-light mesons within basis light-front quantization. The resulting mass spectra of D, D_s, B, and B_s agree reasonably well with experiments. We also predict states which could be measured in the near future. In the light-front formalism, we calculate the light-front wave functions and additional experimental observables, such as parton distribution functions, distribution amplitudes, and decay constants by means of integrations over light-front wave functions. We also provide ratios of decay constants for selected pseudoscalar meson decays (D_s to D and B_s to B) as they may prove to be theoretically more robust and more reliably determined in experiments. We find that our ratios are systematically smaller than existing experiments and other approaches by 5–18%.

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_\perp$, and it deviates from the perturbative calculation at small $p_\perp$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_\perp$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

Basis light-front quantization for a chiral nucleon-pion Lagrangian

We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.

Pion and kaon parton distribution functions from basis light front quantization and QCD evolution

We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu--Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion structure function calculated from the PDFs agrees with the ZEUS and the H1 experiments at DESY-HERA for large $x$. Additionally, the ratio of the up quark PDF of the kaon to that of the pion is in agreement with the NA-003 experiment at CERN. We also present the cross section for the pion-nucleus induced Drell-Yan process with the obtained pion PDFs supplemented by the PDFs of the target nuclei.

Heavy quarkonia production at energies available at the CERN Large Hadron Collider and future electron-ion colliding facilities using basis light-front quantization wave functions

We study exclusive charmonium and bottomonium production in ultra-peripheral heavy-ion collisions and electron-ion collisions within the dipole picture. We employ heavy quarkonium light-front wavefunctions obtained within the basis light-front quantization framework, which has some features of the light-front holographic QCD. We focus on comparison with measurements of exclusive charmonium and bottomonium production in ultraperipheral $pp$, $p$Pb and PbPb collisions at LHC and find reasonable agreement with the cross sections. We also discuss the coherent production cross-section ratios of excited states to the ground state for charmonium and bottomonium, which exhibit insensitivity to the dipole model parameters. We show that electron-ion collisions provide an opportunity for a quantitative study of heavy quarkonium structure.

Form factors and generalized parton distributions of heavy quarkonia in basis light front quantization

We calculate the electromagnetic (charge, magnetic and quadrupole) form factors and the associated static moments of heavy quarkonia (charmonia and bottomonia) using the Basis Light Front Quantization (BLFQ) approach. For this work, we adopt light front wavefunctions (LFWFs) generated by a holographic QCD confining potential and a one-gluon exchange interaction with fixed coupling. We compare our BLFQ results with the limiting case of a single BLFQ basis state description of heavy quarkonia and with other available results. These comparisons provide insights into relativistic effects. Using the same LFWFs generated in the BLFQ approach, we also present the generalized parton distributions (GPDs) for selected mesons including those for radially excited mesons such as $\psi^\prime$ and $\Upsilon^\prime$. Our GPD results establish the foundation within BLFQ for further investigating hadronic structure such as probing the spin structure of spin-one hadrons in the off-forward limit.

Basis light front quantization for the charged light mesons with color singlet Nambu–Jona-Lasinio interactions

We apply the basis light front quantization (BLFQ) approach to describe the valence structures of the charged light meson ground states. Specifically, the light front wavefunctions of $\pi^\pm$, $\rho^\pm$, $K^\pm$, and $K^{*\pm}$ are obtained as the eigenvectors of the light front effective Hamiltonians with confinement potentials supplemented by the color singlet Nambu--Jona-Lasinio (NJL) interactions. We adjust our model such that the spectrum of these ground states and the charge radii of the pseudoscalar states agree with experimental results. We present the elastic form factors and parton distribution amplitudes (PDAs) as illustrations of the internal structures of the pseudoscalar pions and kaons in terms of valence quarks.

Radiative transitions between 0−+ and 1−− heavy quarkonia on the light front

We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" $J^+$ and the transverse current $\vec J_\perp$ (in particular, $J^R=J^x+i J^y$). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections ($m_j=0,\pm 1$). We use the $m_j=0$ state of the vector meson to obtain the transition form factor, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. While the $m_j=\pm 1$ states are also examined, transition form factors depend on subdominant components of the light-front wavefunctions and are less robust. Transitions between states below the open-flavor thresholds are computed, including those for excited states. Comparisons are made with the experimental measurements as well as with Lattice QCD and quark model results. In addition, we apply the transverse current to calculate the decay constant of vector mesons where we obtain consistent results using either $m_j=0$ or $m_j=1$ light-front wavefunctions. This consistency provides evidence for features of rotational symmetry within the model.

Hadron Spectra, Decays and Scattering Properties Within Basis Light Front Quantization

We survey recent progress in calculating properties of the electron and hadrons within the Basis Light Front Quantization (BLFQ) approach. We include applications to electromagnetic and strong scattering processes in relativistic heavy ion collisions. We present an initial investigation into the glueball states by applying BLFQ with multigluon sectors, introducing future research possibilities on multi-quark and multi-gluon systems.

Exclusive J/ψ photoproduction in a diffractive process using the AdS/QCD holographic wave function in BLFQ

AdS/QCD is implemented to calculate the basis light-front quantization (BLFQ) wave function for [Formula: see text] meson. Exclusive [Formula: see text] photoproduction is computed in the dipole picture using this holographic wave function. The bCGC model is employed in the calculation of [Formula: see text] production for dipole amplitude. The differential cross-sections and total cross-sections of [Formula: see text] meson are computed and compared with the experimental data. We find that the AdS/QCD holographic wave function in BLFQ can be employed as a new candidate for the light-front wave function of [Formula: see text] meson in diffractive process.