Light-front Approach Research Articles

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.

Heavy quark contribution to the electromagnetic properties of the nucleon

Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form factors, distribution amplitudes, structure functions, etc. We will extend this nonperturbative light-front QCD approach to study the heavy quark-antiquark contribution to the electromagnetic properties of nucleon. Our framework is based on a study of the eigenfunctions of the QCD light-front Hamiltonian, the frame-independent light-front wave functions (LFWFs) underlying hadron dynamics. We analyze the heavy quark content in the proton, induced either directly by the nonperturbative $|uud+Q\bar Q\rangle$ Fock state or by the $|uud+g\rangle$ Fock state, where the gluon splits into a heavy quark-antiquark pair. The specific form of these LFWFs are derived from LFHQCD. Using these LFWFs, we construct light-front representations for the heavy quark-antiquark asymmetry, the electromagnetic form factors of nucleons induced by heavy quarks, including their magnetic moments and radii.

Insights into the nature of X(3872) through B meson decays* *Supported by the National Natural Science Foundation of China (11347030) and the Program of Science and Technology Innovation Talents in Universities of Henan Province (14HASTIT037)

We study the decays in the perturbative QCD (PQCD) approach, involving the puzzling resonance , where P represents a light pseudoscalar meson (K or π). Assuming to be a charmonium state, we obtain the following results. (a) The branching ratios of the and decays are consistent with the results predicted by the covariant light-front approach within errors; however, they are larger than those given by the generalized factorization approach. (b) The branching ratio of the decay is predicted as , which is smaller than the previous PQCD calculation result but still slightly larger than the upper limits set by Belle and BaBar. Hence, we suggest that the decays should be precisely measured by the LHCb and Belle II experiments to help probe the inner structure of . (c) Compared with the decays, the decays have significantly smaller branching ratios, which drop to values as low as . (d) The direct CP violations of these considered decays are small () because the penguin contributions are loop suppressed compared to the tree contributions. The mixing-induced CP violation of the decay is highly consistent with the current world average value %. Experimentally testing the results for the branching ratios and CP violations, including the implicit and isospin symmetries of these decays, helps probe the nature of .

Light-front approach to axial-vector quarkonium γ*γ* form factors

In this work, we perform a detailed study of transition form factors for axial- vector meson production via the two-photon fusion process γ*γ* → 1++, with space-like virtual photons in the initial state and a P-wave axial-vector quarkonium in the final state. In this analysis, we employ the formalism of light-front quarkonium wave functions obtained from a solution of the Schrödinger equation for a selection of interquark potentials for Qoverline{Q} interaction. We found the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any qoverline{q} axial-vector meson γ*γ* → 1++ transition, while our numerical results are given for the phenomenologically relevant charmonium χc1 state. We present the helicity form factors as functions of both photon virtualities. We also obtain, that QFLT(Q2, 0)/FTT(Q2, 0) = const.

Weak decays of triply heavy baryons in light front approach

We analyze weak decays of triply heavy baryon Ωccc++ and calculate the form factors for Ωccc++→Ξcc++/Ωcc+ transitions in a light front quark model. The momentum distributions in form factors are accessed via the pole-model parametrization. Using the results for form factors, we predict decay branching fractions for semi-leptonic decays, and obtain B(Ωccc++→Ξcc+e+νe)=0.08%, B(Ωccc++→Ωcc+e+νe)=1.23%. Forward-backward asymmetry and angular distributions are then investigated in this work. We also estimate branching fractions for a few color-allowed processes and find that the Ωccc++→Ωcc+π+ has a sizable branching fraction: B(Ωccc++→Ωcc+π+)=1.82%. We point out that the Ωccc++→Ωcc+π+ is a golden channel for the discovery of the Ωccc++. This analysis can provide a useful reference for future experimental search in future.

Analysis of FCNC ΞQQ→ΛQl+l− decay in light-cone sum rules

The weak decays of doubly heavy ${\mathrm{\ensuremath{\Xi}}}_{QQ}$ baryon induced by flavor changing $b\ensuremath{\rightarrow}d$ and $c\ensuremath{\rightarrow}u$ flavor changing neutral current within the light-cone sum rules are studied. The sum rules are constructed and analyzed for the corresponding transition form factors using the parallel components of the light-cone distribution amplitudes for ${\mathrm{\ensuremath{\Lambda}}}_{Q}$ baryon. Having the results for the form factors, the corresponding branching ratios for ${\mathrm{\ensuremath{\Xi}}}_{QQ}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{Q}{l}^{+}{l}^{\ensuremath{-}}$ decays are estimated. While the branching ratio due to $b\ensuremath{\rightarrow}d$ transition is around ${10}^{\ensuremath{-}9}$, in $c\ensuremath{\rightarrow}u$ transition case, it is found as around ${10}^{\ensuremath{-}13}$. Hence, ${\mathrm{\ensuremath{\Xi}}}_{bb}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}{l}^{+}{l}^{\ensuremath{-}}$ decay has the potential of being discovered at LHCb. However, ${\mathrm{\ensuremath{\Xi}}}_{bb}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}{l}^{+}{l}^{\ensuremath{-}}$ is difficult to be measured due to the extremely small values of obtained branching ratio. Our results on the branching ratio are also compared with the results of the light-front approach.

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.

Bound States in QED from a light-front approach


 We calculate the binding energy and structure of the positronium system in a light-front nonperturbative approach. The input interaction is from Quantum Electrodynamics first principles and one dynamical photon is explicitly included in the basis. We obtain the low-lying mass spectrum, which is found to be consistent with that from nonrelativistic quantum mechanics. Various excitation modes of the low-lying states can be identified from the associated wave functions. The photon distribution in the longitudinal direction is calculated for the low-lying positronium states.

Chiral Symmetry Restoration Using the Running Coupling Constant from the Light-Front Approach to QCD

In this work, the distance between a quark-antiquark pair is analyzed through both the confinement potential and the hadronic total cross- section. Using the Helmholtz free energy, the entropy is calculated near the minimum of the total cross-section through the confinement potential. A fitting procedure for the proton-proton total cross- section is carried out, defining the fit parameters. Therefore, the only remaining free parameter in the model is the mass-scale к used to define the running coupling constant of the light-front the approach to QCD. The mass scale controls the distance r between the quark-antiquark pair and, under some conditions, allows the appearance of free quarks even within the confinement regime of QCD.

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

Two-photon transitions of charmonia on the light front

We investigate the two-photon transitions $H_{c\bar c} \to \gamma^*\gamma$ of the charmonium system in light-front dynamics. The light-front wave functions were obtained from solving the effective Hamiltonian based on light-front holography and one-gluon exchange interaction within the basis light-front quantization approach. We compute the two-photon transition form factors as well as the two-photon decay widths for S- and P-wave charmonia, $\eta_c$ and $\chi_{cJ}$ and their excitations. Without introducing any free parameters, our predictions are in good agreement with the recent experimental measurements by BaBar and Belle, shedding light on the relativistic nature of charmonium.

Residual mean field model of valence quarks in the nucleon

We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark–quark interactions that generate the high x tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, x_p, of the peak of xq_V(x) distribution of the valence quark and the effective mass of the residual system, m_R, in the form: x_{p} approx {1over 4} (1-{m_Rover m_N}) at starting Q^2. This relation explains the difference in the peak positions for d- and u-quarks through the expected difference of residual masses for valence d- and u-quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u-quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.

Gravitational form factors and mechanical properties of a quark at one loop in light-front Hamiltonian QCD

We calculate the gravitational form factors (GFFs) and pressure, shear, and energy distributions for a quark state dressed with a gluon at one loop in QCD. We use the light-front Hamiltonian approach. In the light-front gauge, we use a two-component formalism to eliminate the constrained fields. The state may be thought of as a perturbative model for a relativistic spin-$1/2$ composite system having a gluonic degree of freedom. We compare the results with model calculations for a nucleon.

Basis light-front quantization approach to photon

We solve for the light-front wave functions (LFWFs) of the physical photon from the eigenvectors of the light-front quantum electrodynamics (QED) Hamiltonian with the aim to determine its bare photon and electron-positron Fock components. We then employ the resulting LFWFs to compute the transverse momentum dependent parton distributions (TMDs) and the generalized parton distributions (GPDs) at zero skewness of the photon. The TMDs are found to be in excellent agreement with the lowest-order perturbative results calculated using the electron-positron quantum fluctuation of the photon. The GPDs are also consistent with the perturbative calculations.

Study of Bu,d,s→K0*(1430)P and K0*(1430)V decays within QCD factorization

We study the nonleptonic charmless ${B}_{u,d,s}\ensuremath{\rightarrow}{K}_{0}^{*}(1430)P$ ($P=K$, $\ensuremath{\pi}$) and ${K}_{0}^{*}(1430)V$ $(V={K}^{*},\ensuremath{\rho},\ensuremath{\omega},\ensuremath{\phi})$ decays. The amplitudes are calculated within the QCD factorization, and the nonperturbative quantities are evaluated by using a covariant light-front approach. The branching fractions and $CP$ asymmetries of theses decay modes are calculated, some decay modes are first predicted, and some useful relations based on $SU(3)$ flavor symmetry are discussed. Comparing the theoretical results with the current available experimental data, it is found that ${K}_{0}^{*}(1430)$ can be described as the lowest-lying p-wave $(s,u/d)$ state rather than the first excited one.

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.

Scattering and gluon emission in a color field: A light-front Hamiltonian approach

We develop a numerical method to nonperturbatively study scattering and gluon emission of a quark from a colored target using a light-front Hamiltonian approach. The target is described as a classical color field, as in the Color Glass Condensate effective theory. The Fock space of the scattering system is restricted to the $\ket{q}+\ket{qg}$ sectors, but the time evolution of this truncated system is solved exactly. This method allows us to study the interplay between coherence and multiple scattering in gluon emission. It could be applied both to studying subeikonal effects in high energy scattering and to understanding jet quenching in a hot plasma.

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.

Light-front approach to relativistic electrodynamics

We illustrate how our recent light-front approach simplifies relativistic electrody-namics with an electromagnetic (EM) field F μν that is the sum of a (even very intense) plane travelling wave and a static part ; it adopts the light-like coordinate ξ = ct – z instead of time t as an independent variable. This can be applied to several cases of extreme acceleration, both in vacuum and in a cold diluted pasma hit by a very short and intense laser pulse (slingshot effect, plasma wave-breaking and lasera wake-field cceleration, etc.)