Light-front Quantization Research Articles

Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach

We compute the gravitational form factors (GFFs) and study their applications for the description of the mechanical properties such as the pressure, shear force distributions, and the mechanical radius of the proton from its light-front wave functions (LFWFs) based on basis light-front quantization (BLFQ). The LFWFs of the proton are given by the lowest eigenvector of a light-front effective Hamiltonian that incorporates a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling between the constituent quarks solved in the valence Fock sector. We find acceptable agreement between our BLFQ computations and the lattice QCD for the GFFs. Our D-term form factor also agrees well with the extracted data from the deeply virtual Compton scattering experiments at Jefferson Lab, and the results of different phenomenological models. The distributions of pressures and shear forces are similar to those from different models. Published by the American Physical Society 2024

Euclidean effective theory for partons in the spirit of Steven Weinberg

The standard formulation of parton physics involves light-cone correlations of quark and gluon fields in a hadron, which leads to a widespread impression that it can only be studied through real-time Hamiltonian dynamics or light-front quantization, which are challenged by non-perturbative computations with a pertinent regulator for light-cone/rapidity divergences (or zero modes). As such, standard lattice QCD studies have been limited to indirect parton observables such as first few moments and short-distance correlations, which do not provide the x-distributions without solving the model-dependent inverse problem. Here I describe an alternative formulation of partons in terms of equal-time (or Euclidean) correlators, which allows to compute precision-controlled x-distribution through lattice QCD simulations. This approach is in accord with Weinberg's pioneering idea of effective field theory as well as Wilson's renormalization group, in which the large hadron momentum serves as a natural cut-off for light-cone/rapidity divergences and can ultimately be eliminated through a method like the “perfect action” program in lattice QCD.

Transverse-momentum-dependent gluon distributions of proton within basis light-front quantization

Gluon transverse-momentum dependent distributions (TMDs) are very important for revealing the internal structure of the proton. They correspond to a variety of experiments and are among the major tasks of the future electron-ion colliders. In this paper, we calculate the T-even gluon TMDs at the leading twist within the Basis Light-front Quantization framework. We employ the light-front wave functions of the proton obtained from a light-front quantized Hamiltonian with Quantum Chromodynamics input determined for its valence Fock-sector with three constituent quarks and an additional Fock-sector, encompassing three quarks and a dynamical gluon, with a three-dimensional confinement. After obtaining the numerical results we investigate the properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues inequalities and investigate the correlations between transverse and longitudinal degrees of freedom. With their connection to unintegrated gluon distributions in mind, we further investigate the limiting behaviors of gluon TMDs in the small-x and large-x regions.

Skewed generalized parton distributions of proton from basis light-front quantization

We obtain all the leading-twist quark generalized parton distributions (GPDs) inside the proton at nonzero skewness within the basis light-front quantization framework. We employ the light-front wave functions of the proton from a light-front quantized Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. We find that the qualitative behaviors of our GPDs are similar to those of other theoretical calculations. We further examine the GPDs within the boost-invariant longitudinal coordinate, σ=12b−P+, which is identified as the Fourier conjugate of the skewness. The GPDs in the σ-space show diffraction patterns, which are akin to the diffractive scattering of a wave in optics.

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T++ and T+−, which are used to extract the gravitational form factors A(Q2) and D(Q2). The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

Quark and gluon distributions in ρ-meson from basis light-front quantization

We solve for the ρ-meson's wave functions from a light-front QCD Hamiltonian determined for its constituent quark-antiquark and quark-antiquark-gluon Fock components, with a three-dimensional confinement using basis light-front quantization. From this, we obtain the leading-twist valence quark's parton distribution functions and transverse momentum-dependent parton distributions inside the ρ-meson. These results are qualitatively consistent with those of other models. We also demonstrate the important effects of a dynamical gluon on the ρ-meson's gluon densities, helicity, transversity, and tensor polarized distributions.

Twist-3 generalized parton distribution for the proton from basis light-front quantization

We investigate the twist-3 generalized parton distributions (GPDs) for the valence quarks of the proton within the basis light-front quantization (BLFQ) framework. We first solve for the mass spectra and light-front waved functions (LFWFs) in the leading Fock sector using an effective Hamiltonian. Using the LFWFs we then calculate the twist-3 GPDs via the overlap representation. By taking the forward limit, we also get the twist-3 parton distribution functions (PDFs), and discuss their properties. Our prediction for the twist-3 scalar PDF agrees well with the CLAS experimental extractions. Published by the American Physical Society 2024

Leading twist T -even TMDs for the spin-1 heavy vector mesons

We have presented the leading twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 heavy vector mesons J/ψ-meson and ϒ-meson using the overlap of the light-front wave functions. We have computed their TMDs in the light-front holographic model (LFHM) as well as the light-front quark model (LFQM) and further compared the results with the Bethe-Salpeter (BSE) model. We have discussed the behavior of the TMDs with respect to momentum fraction carried by active quark (x) and the transverse quark momenta (k⊥) in both the models. We have also calculated the k⊥ moments of the quark in both the models and have compared the results with the BSE model. The predictions of LFQM are found to be in accord with the BSE model. Further, we have analyzed the leading twist parton distribution functions (PDFs) for both the heavy mesons in both the models and the results are found to be in accord with the basic light-front quantization (BLFQ) and BSE model. Published by the American Physical Society 2024

Light-cone and quasigeneralized parton distributions in the ’t Hooft model

We present a comprehensive study of the light-cone generalized parton distribution (GPD) and quasi-GPD of a flavor-neutral meson in the ’t Hooft model, i.e., two-dimensional QCD (QCD2) in the Nc→∞ limit. With the aid of the Hamiltonian approach, we construct the light-cone GPD in terms of the meson’s light-cone wave function in the framework of light-front quantization and express the quasi-GPD in terms of the meson’s Bars-Green wave functions and the chiral angle in the framework of equal-time quantization. We show that, both analytically and numerically, the quasi-GPD does approach the light-cone GPD when the meson is boosted to the infinite momentum frame, which justifies the tenet underlying the large momentum effective theory for the off-forward parton distribution. Upon taking the forward limit, the light-cone and quasi-GPDs reduce to the light-cone and quasi parton distribution functions (quasi-PDFs). As a bonus, we take this chance to correct the incomplete expression of the quasi-PDFs in the ’t Hooft model reported in our preceding work [Y. Jia , ]. Published by the American Physical Society 2024

Spatial imaging of proton via leading-twist nonskewed GPDs with basis light-front quantization

The internal image of the proton is unveiled by examining the generalized parton distributions (GPDs) at zero skewness, within the basis light-front quantized environment. Several distributions emerge when a quark is sampled with different currents depending upon the helicity arrangements of the active quark and the proton target. We investigate six of the eight leading-twist proton GPDs of the valence quarks, the helicity conserving distributions (H,E,H˜) and the helicity nonconserving (HT,ET,H˜T) distributions at skewness set to zero (ζ=0). We consider purely transverse momentum transfer and, hence, obtain results describe only the proton’s two-dimensional structure in the transverse plane. We present the Mellin moments of these distribution functions, where the first moment produces a form factor and the second Mellin moments help extract the information on partonic contributions to the hadronic angular momentum. We compare our results for the Mellin moments with those from lattice QCD and other approaches where available. We also present the GPDs in transverse position space. Published by the American Physical Society 2024

Light-front puzzles

Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

Massless and massive photons within basis light-front quantization

Massless and massive photons within basis light-front quantization

Generalized parton distributions of gluon in proton: A light-front quantization approach

We solve for the gluon generalized parton distributions (GPDs) inside the proton at zero skewness, focusing specifically on leading twist chiral-even GPDs. We obtain and employ the light-front wavefunctions (LFWFs) of the proton from a light-front quantized Hamiltonian with Quantum Chromodynamics input using basis light-front quantization (BLFQ). Our investigation incorporates the valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon. We examine the GPDs within impact parameter space and evaluate the x-dependence of the transverse square radius. We find that the transverse size of the gluon at lower-x is larger than that of the quark, while it exhibits opposite behavior at large-x. Using the proton spin sum rule, we also determine the relative contributions of quarks and the gluon to the total angular momentum of the proton.

Anisotropic flow and the valence quark skeleton of hadrons

We study transverse momentum anisotropies, in particular, the elliptic flow v2 due to the interference effect sourced by valence quarks in high-energy hadron-hadron collisions. Our main formula is derived as the high-energy (eikonal) limit of the impact-parameter dependent cross section in quantum field theory, which agrees with that in terms of the impact parameter in the classical picture. As a quantitative assessment of the interference effect, we calculate v2 in the azimuthal distribution of gluons at a comprehensive coverage of the impact parameter and the transverse momentum in high-energy pion-pion collisions. In a broad range of the impact parameter, a sizable amount of v2, comparable with that produced due to saturated dense gluons or final-state interactions, is found to develop. This is in contrast with similar studies in heavy-ion collisions using classical color charge distributions in which such a contribution from geometric correlations was found to be small and has, hence, been ignored in recent studies. In our calculations, the valence sector of the pion wave function is obtained numerically from the Basis Light-Front Quantization, a non-perturbative light-front Hamiltonian approach. And our formalism is generic and can be applied to other small collision systems like proton-proton collisions.

Solving bound state equation for scalar and hybrid QCD in two-dimensional spacetime

Abstract We investigate the bound-state equations in two-dimensional QCD in the $N_c\to \infty$ limit. We consider two types of hadrons, an exotic ``meson" (which is composed of a bosonic quark and a bosonic anti-quark), and an exotic ``baryon" (composed of a fermionic quark and a bosonic antiquark). Using the operator approach, we derive the corresponding bound-state equations for both types of hadrons from the perspectives of light-front quantization and equal-time quantization and confirm the known results. We also present a novel diagrammatic derivation for the exotic meson bound-state equation in the equal-time quantization.Our bound-state equation for the exotic baryons in the equal-time quantization is new. We also numerically solve various bound-state equations, obtain the hadron spectrum and the bound-state wave functions of the lowest-lying states. We explicitly demonstrate the pattern that as the hadron is boosted to infinite-momentum frame, the forward-moving bound-state wave function approach the light-front wave function. 
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Transverse structure of the pion beyond leading twist with basis light-front quantization

We investigate the twist-3 transverse-momentum-dependent parton distribution functions (TMDs) of the pion with basis light-front quantization. The twist-3 TMDs are not independent and can be decomposed into twist-2 and genuine twist-3 terms from the equations of motion (EOM). We compute the TMDs from the resulting light-front wave functions obtained by diagonalizing the light-front QCD Hamiltonian, determined for pion's constituent quark-antiquark and quark-antiquark-gluon Fock sectors, with three-dimensional confinement. We also obtain the twist-3 parton distribution functions (PDFs) and show that they preserve the sum rule, which affirms the robustness of our approach. This is the first time that theoretical predictions are made for subleading twist structures of the pion containing interference terms between two light-front Fock sectors.

Infrared divergences in e+e−→2 jets in the light front coherent state formalism

We study infrared (IR) divergences in light front quantum chromodynamics using a coherent state basis in light front time-ordered Hamiltonian perturbation theory. In computation of the S-matrix elements in Hamiltonian formalism, the IR divergences appear in the form of vanishing energy denominators. We consider the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2$ jets at $\mathcal{O}({g}^{2})$ in strong coupling, construct the coherent state representing the outgoing particles, and explicitly show that the ``true'' IR divergences cancel to this order when the matrix elements are calculated between coherent states instead of Fock states.

Solving hadron structures using the basis light-front quantization approach on quantum computers

Quantum computing has demonstrated the potential to revolutionize our understanding of nuclear, atomic, and molecular structure by obtaining forefront solutions in nonrelativistic quantum many-body theory. In this work, we show that quantum computing can be used to solve for the structure of hadrons, governed by strongly interacting relativistic quantum field theory. Following our previous work on light unflavored mesons as a relativistic bound-state problem within the nonperturbative Hamiltonian formalism, we present the numerical calculations on simulated quantum devices using the basis light-front quantization approach. We implement and compare the variational quantum eigensolver and the subspace-search variational quantum eigensolver to find the low-lying mass spectrum of the light meson system and its corresponding light-front wave functions as quantum states from ideal simulators, noisy simulators, and IBM quantum computers. Based on obtained quantum states, we evaluate the meson decay constants and parton distribution functions directly on the quantum circuits. Our calculations on the quantum computers and simulators are in reasonable agreement with accurate numerical solutions solved on classical computers when noises are moderately small, and our overall results are comparable with the available experimental data.

Hadron structure from basis light-front quantization

We present our recent progress in applying basis light-front quantization approach to investigate the structure of the light mesons and the nucleon.

Transverse momentum structure of proton within the basis light-front quantization framework

We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extensive treatments of QCD. Furthermore, we obtain a non-trivial x-dependence of the 〈(p⊥)2〉 and some consistency with the Gaussian ansatz but only in the small (p⊥)2 region. Those features suggest our results may be a useful alternative in future experimental extractions.