Light-front Formalism Research Articles

χc2 tensor meson transition form factors in the light front approach

We continue our work on the light-front formulation of quarkonium γ∗γ transition form factors, extending the formalism to JPC = 2++ tensor meson states. We present an analysis of γ∗γ → χc2 transition amplitude and the pertinent helicity form factors. Our relativistic formalism is based on the light-front quark-antiquark wave function of the quarkonium. We calculate the two-photon decay width as well as three independent γ∗γ transition form factors for Jz = 0, 1, 2 as a function of photon virtuality Q2. We compare our results for the two-photon decay width to the recently measured ones by the Belle and BES III collaborations. Even when including relativistic corrections, a very small Γ(λ = 0)/Γ(λ = 2) ~ 10−3 ratio is found which is beyond present experimental precision. We also present the form factors as a function of photon virtuality and compare them to the sparse experimental data on the so-called off-shell width. The formalism presented here can be used for other 2++ mesons, excited charmonia or bottomonia or even light qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document}-mesons.

The spin alignment of vector mesons with light front quarks

The global spin alignment of the vector meson has been observed in relativistic heavy ion collisions, but its theoretical origin is still on hot debates. Here we propose to apply the light front framework to explain this phenomenon since the light front form explicitly describes the hadron spin including both the quark spin and the orbital angular momentum. After applying the light front spinor, we find that the spin alignment in the polarization of vector mesons with ρ00>1/3 can be naturally manifested and in particular, the obtained spin alignment for ϕ meson is in good agreement with the experimental data. This implies that to explain the spin alignment it is important to properly include the contribution from the gluon interactions that are presented in terms of the orbital angular momentum of the hadron bound state.

Effective potential between static sources in quenched light-front Yukawa theory

We compute a nonperturbative effective potential between two static fermions in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair production is suppressed, to make possible an exact analytic solution in the form of a coherent state of bosons that form clouds around the sources. The effective potential is essentially an interference term between individual clouds. The model is regulated with Pauli-Villars bosons and fermions, to achieve consistent quantization and renormalization of masses and couplings. This extends earlier work on scalar Yukawa theory where Pauli-Villars regularization did not play a central role. The key result is that the nonperturbative solution restores rotational symmetry even though the light-front formulation of Yukawa theory, with its preferred axis, appears antithetical to such a symmetry. Published by the American Physical Society 2024

The EMC effect for few-nucleon bound systems in light-front Hamiltonian dynamics

The light-front formalism for a covariant description of the European Muon Collaboration (EMC) effect, already applied to He3, is formally extended to any nucleus, and used for actually calculating the 3H and He4 cases. The realistic and accurate nuclear description of few-nucleon bound systems, obtained with both phenomenological and chiral potentials, has been properly combined with the Poincaré covariance and macroscopic locality, automatically satisfying both number of particles and momentum sum rule. While retaining the on-mass-shell nucleon structure functions, one is then able to predict a sizable EMC effect for He4, as already observed for He3. Moreover, the impact on the EMC effect of both i) the short-range correlations, such as those generated by modern nuclear interactions, and ii) the ratio between the neutron and proton structure functions has been studied. The short-range correlations generated by retaining only the standard nuclear degrees of freedom act on the depth of the minimum in the EMC ratio, while the uncertainties linked to the ratio of neutron to proton structure functions are found to be very small. These light-front results facilitate ascribing deviations from experimental data due to genuine QCD effects, not included in a standard nuclear description, and initiating unbiased investigations.

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.

Dirac equation solution in the light front via linear algebra and its particularities

In undergraduate and postgraduate courses, it is customary to present the Dirac equation defined in a space of four dimensions: three spatial and one temporal. This article discusses aspects of the Dirac equation (QED) on the light front. This proposal of coordinate transformations comes from Dirac who originally introduced three distinct forms of relativistic dynamics possible depending on the choice we make of the different hypersurfaces constant in time. The first he called instantaneous, the most common form, the hypersurface of which is specified by the boundary conditions set at . The second, known as the point form, has as its characterizing surface, a hyperboloid, described by the initial conditions in , being one constant (chosen as the time of this system). The third relativistic form, known as the light front form, has its hypersurface tangent to the light cone; being defined by the initial conditions at , and is the time in the light front system. The method of this work is deductive. Therefore, one obtains the solution of the Dirac equation for the Free Electron and for the positron in the coordinates in the light front with the particularity of the energy associated with the system being given by , and for moments we have the electron and we have the positron. The result of this is that the positive energy states in the light front and negative are independently described in the equation, and with additional, the problem at the limit that does not converge.

Light front synchronization and rest frame densities of the proton: Electromagnetic densities

We clarify the physical origin and meaning of the two-dimensional relativistic densities of the light front formalism. The densities are shown to originate entirely from the use of light front time instead of instant form time, which physically corresponds to using an alternative synchronization convention. This is shown by using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates, and which are also used to show that the obtained densities describe a system at rest rather than at infinite momentum. These coordinates allow all four components of the electromagnetic current density to be given clear physical meanings. We explicate the formalism for spin-half targets, obtaining charge and current densities of the proton and neutron using empirical form factor parametrizations, as well as up and down quark densities and currents. Angular modulations in the densities of transversely polarized states are explained as originating from redshifts and blueshifts due to quarks moving in different longitudinal directions.

The European Muon Collaboration effect in light-front Hamiltonian dynamics

A new and rigorous light-front formalism for electron deep inelastic scattering on unpolarized nuclei, in Bjorken limit, is proposed. It preserves Poincaré covariance, macroscopic locality, both number of particles and momentum sum rules. The approach is applied to the A=3 iso-doublet, very relevant for the flavor decomposition of the parton distribution functions and in view of the planned operation with unpolarized and polarized beams at the Electron-Ion Collider. At variance with previous light-front estimates, our procedure, including a realistic nuclear description and free-nucleon structure functions, predicts a sizable European Muon Collaboration effect for 3He. This will allow to analyze deviations from the proposed baseline in terms of genuine QCD effects. The extension to heavier nuclei is straightforward, although numerically challenging.

Hadronic structure on the light front. II. QCD strings, Wilson lines, and potentials

This is the second paper on hadronic wave functions in the light-front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light-cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the light front.

Pion and nucleon relativistic electromagnetic four-current distributions

The quantum phase-space approach allows one to define relativistic spatial distributions inside a target with arbitrary spin and arbitrary average momentum. We apply this quasiprobabilistic formalism to the whole electromagnetic four-current operator in the case of spin-0 and spin-$\frac{1}{2}$ targets, study in detail the frame dependence of the corresponding spatial distributions, and compare our results with those from the light-front formalism. While former works focused on the charge distributions, we extend here the investigations to the current distributions. We clarify the role played by the Wigner rotation and argue that electromagnetic properties are most naturally understood in terms of Sachs form factors, contrary to what the light-front formalism previously suggested. Finally, we illustrate our results using the pion and nucleon electromagnetic form factors extracted from experimental data.

Spatial densities of momentum and forces in spin-one hadrons

Densities associated with the energy-momentum tensor are calculated for spin-one targets. These calculations are done in a light front formalism, which accounts for relativistic effects due to boosts and allows for arbitrary spatial localization of the target. These densities include the distribution of momentum, angular momentum, and pressures over a two-dimensional plane transverse to the light front. Results are obtained for both longitudinally and transversely polarized targets, and the formalism is tailored to allow the possibility of massless targets. The momentum density and pressure distributions are calculated for a deuteron target in a light cone convolution model, with which the properties of this model (such as helicity dependence of the densities) is illustrated.

Light-front description of infinite spin fields in six-dimensional Minkowski space

We present a new 6D infinite spin field theory in the light-front formulation. The Lorentz-covariant counterparts of these fields depend on 6-vector coordinates and additional spinor variables. Casimir operators in this realization are found. We obtain infinite-spin fields in the light-cone frame which depend on two sets of the mathrm {SU}(2)-harmonic variables. The generators of the 6D Poincaré group and the infinite spin field action in the light-front formulation are presented.

Light front wave functions from AdS/QCD models

In this talk, we present an extension to the matching procedure proposed by Brodsky and de Teramond to obtain the two-body wave functions in the light-front formalism for holographic models. We consider different static dilaton fields and AdS-like geometric deformations.

Momentum transfer dependence of heavy quarkonium electroproduction

We investigate the momentum transfer dependence of differential cross sections d\sigma/dtdσ/dt in diffractive electroproduction of heavy quarkonia on proton targets. Model predictions for d\sigma/dtdσ/dt within the light-front QCD dipole formalism are based on a realistic model for a proper correlation between the impact parameter \vec bb⃗ of a collision and color dipole orientation \vec rr⃗. We demonstrate a significance of \vec b-\vec rb⃗−r⃗ correlation by comparing with a standard simplification \vec{b}\parallel\vec{r}b⃗∥r⃗, frequently used in the literature.

Impact parameter dependence of color charge correlations in the proton

The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the |qqqg\rangle|qqqg⟩ Fock state via light-cone perturbation theory. Near the center of the proton, the bb-dependence of the correlations is very different from a ``transverse profile function’’. The resulting tt-dependence of exclusive J/\PsiJ/Ψ photoproduction transitions from exponential to power law at |t| \approx 1|t|≈1~GeV^22. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).

Quantum simulation of quantum field theory in the light-front formulation

Quantum chromodynamics (QCD) describes the structure of hadrons such as the proton at a fundamental level. The precision of calculations in QCD limits the precision of the values of many physical parameters extracted from collider data. For example, uncertainty in the parton distribution function (PDF) is the dominant source of error in the $W$ mass measurement at the LHC. Improving the precision of such measurements is essential in the search for new physics. Quantum simulation offers an efficient way of studying quantum field theories (QFTs) such as QCD non-perturbatively. Previous quantum algorithms for simulating QFTs have qubit requirements that are well beyond the most ambitious experimental proposals for large-scale quantum computers. Can the qubit requirements for such algorithms be brought into range of quantum computation with several thousand logical qubits? We show how this can be achieved by using the light-front formulation of quantum field theory. This work was inspired by the similarity of the light-front formulation to quantum chemistry, first noted by Kenneth Wilson.

Algebra of discrete symmetries in the extended Poincaré group

We begin with the comprehensible review of the basics of the Lorentz, (extended) Poincare Groups and O(3,2) and O(4,1). On the basis of the Gelfand-Tsetlin-Sokolik-Silagadze research [1-3], we investigate the definitions of the discrete symmetry operators both on the classical level, and in the secondary-quantization scheme. We studied the physical content within several bases: light-front form formulation, helicity basis, angular momentum basis, on several practical examples. The conclusion is that we have ambiguities in the definitions of the the corresponding operators P, C; T, which lead to different physical consequences.

Pion electromagnetic form factor with Minkowskian dynamics

The pion electromagnetic form factor has been calculated for the first time from the solutions of the Bethe-Salpeter equation, obtained directly in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The one-gluon exchange kernel contains as inputs the quark and gluon masses, as well as a scale parameter featuring the extended quark-gluon vertex. The range of variability of these parameters is suggested by lattice calculations. After presenting a very successful comparison with the existing data in the whole range of the momentum transfer, we show how inserting the light-front (LF) formalism in our approach allows to achieve further interesting results, like the evaluation of the LF valence form factor and a first investigation of the end-points effects.

Forces within hadrons on the light front

In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.

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.