Light-front Quantization Research Articles

Nucleon structure from a light-front hamiltonian


 
 
 We obtain the light-front wave functions (LFWFs) of the nucleon in the leading Fock sector representation using basis light-front quantization (BLFQ) approach. We adopt a light-front effective Hamiltonian, which includes a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling, and solve for it mass eigenstates. We then employ the LFWFs to compute the axial form factor and the transverse charge and magnetization densities for the nucleon. The axial form factor is found to be consistent with the experimental data. The charge and magnetization densities agree qualitatively with the phenomenological fits.
 
 

Tadpoles and vacuum bubbles in light-front quantization

We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations. These transitions also dictate a nontrivial vacuum and contributions from vacuum bubbles to physical states. In nonperturbative calculations these separate classes of contributions (tadpoles and bubbles) cannot be filtered; instead, we regulate the bubbles and subtract the vacuum energy from the eigenenergy of physical states. The key is replacement of momentum-conserving delta functions with model functions of finite width; the width becomes the regulator and is removed after subtractions. The approach is illustrated in free scalar theory, in quenched scalar Yukawa theory, and in a limited Fock-space truncation of ${\ensuremath{\phi}}^{4}$ theory.

BLFQ calculations of the proton leading twist quark TMDs


 
 
 For hadron collisions, transverse-momentum-dependent parton distribution functions (TMD PDFs) are important quantities to connect the- oretic calculations and experimental cross sections. And recently, basis light-front quantization (BLFQ) has become a powerful tool to investigate the structures of the bound state. We present the first calculations within the BLFQ framework for the leading twist quark TMDs under a trivial assumption of the gauge link. We compare our calculations with previous calculations via the PDF limit and evolve our results of the unpolarized TMDs.
 
 

All-charm tetraquark in front form dynamics

We study all-charm tetraquarks in the front form of Hamiltonian dynamics using the many-body basis function approach known as basis light-front quantization. The model Hamiltonian contains transverse and longitudinal confining potentials and a one-gluon-exchange effective potential. We calculate masses of two-charm-two-anticharm states focusing on the lowest state. We also calculate two-quark and four-quark estimates of meson-meson breakup threshold. The results suggest that the lowest two-charm-two-anticharm state is not a tightly bound tetraquark. We discuss implications of the cluster decomposition principle for theories formulated on the light front and present our treatment of identical particles together with color-singlet restrictions on the space of quantum states.

Angular momentum and generalized parton distributions for the proton with basis light-front quantization

We study the unpolarized and the helicity-dependent generalized parton distributions (GPDs) for the valence quarks of the proton in both momentum space and position space within the basis light-front quantization (BLFQ) framework. The GPDs for the valence quarks are computed from the eigenvectors of a light-front effective Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. Employing these GPDs, we obtain the spatial distributions of quark angular momentum inside the proton. In our BLFQ approach, we explore various definitions of angular momentum density and illustrate the differences between them arising from terms that integrate to zero. We also discuss the flavor contributions to the quark angular momentum densities.

Artificial dynamical effects in quantum field theory

In Newtonian mechanics, inertial pseudoforces - or fictitious forces - appear in systems studied in non-Galilean reference frames; e.g., a centrifugal force seems to arise if the dynamics is analyzed in a rotating reference frame. The equivalent of Galilean invariance for relativistic kinematics is Poincar\'e invariance; analogous artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework violating Poincar\'e invariance. We highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. In fact, if the system involves the strong interaction, obtaining objective results can become an intractable problem using canonical quantization because the pseudoforces are essentially nonperturbative. In contrast, the treatment of the same problem using light-front (LF) quantization is free of spurious pseudoeffects because Poincar\'e invariance is manifest; thus the treatment of strong interaction problems becomes simpler. These statements are illustrated using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant.

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.

Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory

We compute an effective potential between two fixed sources in light-front quantization of a quenched scalar Yukawa theory that models the interaction of complex scalar fields through the exchange of a neutral scalar. Despite the breaking of explicit rotational symmetry by the use of light-front coordinates, the effective potential is rotationally symmetric and matches the standard Yukawa potential for scalar exchange. The neutral scalar field is represented by a coherent state, which is obtained nonperturbatively as an eigenstate of our model Hamiltonian, with the eigenenergy determining the effective potential. The sources are represented by wave packets that are fixed with respect to ordinary time, but move in light-front coordinates. The theory is quenched, to remove pair-production processes that would otherwise cause the spectrum to be unbounded from below.

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.

Critical coupling for two-dimensional ϕ4 theory in discretized light-cone quantization

We solve for the critical coupling in the symmetric phase of two-dimensional ${\ensuremath{\phi}}^{4}$ field theory using discretized light-cone quantization. We adopt periodic boundary conditions, neglect the zero mode, and obtain a critical coupling consistent with the critical coupling reported using conformal truncation in light-front quantization. We find a 17% difference from the critical coupling reported with light-front quantization in a symmetric polynomial basis.

Response of the Unruh-DeWitt detector in a gravitational wave background

Applying the techniques of light-front quantization to quantize a scalar field in a monochromatic gravitational wave background, we manage to investigate the response of the Unruh-DeWitt detector coupled to a scalar field in the presence of a gravitational wave for the two cases moving along a free-falling trajectory and a constant-accelerating trajectory. The transition rate of the Unruh-DeWitt detector, in both cases, is different from the result with no gravitational wave, and the leading-order correction due to the gravitational wave survives the long-wavelength limit that formally takes the wavelength of the gravitational wave to infinity. This new effect of the gravitational wave on a quantum system is qualitatively different from that on a classical mechanical system, and cannot be understood in terms of gravitational wave tidal force.

Light mesons with one dynamical gluon on the light front

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 pion's gluon densities can be probed through the pion-nucleus induced J/ψ production data. Our pion parton distribution functions provide excellent agreement with J/ψ production data from widely different experimental conditions.

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.

Quantum simulation of second-quantized Hamiltonians in compact encoding

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the $\phi^4$-theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

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.