Light Front Research Articles

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.

Unpolarized generalized parton distributions of light and heavy vector mesons

We study the leading-twist unpolarized generalized parton distributions (GPDs) of light and heavy vector mesons, i.e., the $\ensuremath{\rho}$, $J/\ensuremath{\psi}$, and $\mathrm{\ensuremath{\Upsilon}}$, at zero skewness. An ansatz incorporating the zero-mode contribution is introduced to modify the light front overlap representation of GPDs. The leading Fock-state light front wave functions of vector mesons from Dyson-Schwinger and Bethe-Salpeter equations approach are then employed to study the meson GPDs. The light front spatial distribution of valence quarks within vector mesons is then studied with the impact parameter dependent GPD. We also investigate the electromagnetic and gravitational form factors, which are the first and second Mellin moments of the GPDs. The light-cone mass radius of $\ensuremath{\rho}$ is determined to be 0.30 fm, close to a recent Nambu-Jona-Lasinio model prediction of 0.32 fm. For $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}$, they are predicted to be 0.151 fm and 0.089 fm respectively.

New Structure in the Deuteron.

We demonstrate that a paradigm shift from considering the deuteron as a system of a bound proton and neutron to that of a pseudovector system in which we observe a proton and neutron results in the possibility of probing a new "incomplete" P-statelike structure on the light front (LF). This occurs at extremely large internal momenta, which can be achieved in a high energy transfer electrodisintegration of the deuteron. Investigating the deuteron on the light front, where the vacuum fluctuations are suppressed, we found that this new structure, together with the conventional S and D states, is leading order in transferred energy of the reaction and thus not suppressed on the light front. The incompleteness of the observed P state results in a violation of the angular condition that can happen only if the deuteron contains non-nucleonic structures, such as Δ Δ, N^{*}N or hidden color components. We demonstrate that experimentally verifiable signatures of incomplete P states are angular anisotropy of the light front momentum distribution of the nucleon in the deuteron, as well as an enhancement of the tensor polarization strength beyond the S- and D-wave predictions at large internal momenta in the deuteron.

Spatial entanglement in two-dimensional QCD: Renyi and Ryu-Takayanagi entropies

We derive a general formula for the replica partition function in the vacuum state, for a large class of interacting theories with fermions, with or without gauge fields, using the equal-time formulation on the light front. The result is used to analyze the spatial entanglement of interacting Dirac fermions in two-dimensional QCD. A particular attention is paid to the issues of infrared cut-off dependence and gauge invariance. The Renyi entropy for a single interval, is given by the rainbow dressed quark propagator to order ${\cal O}(N_c)$. The contributions to order ${\cal O}(1)$, are shown to follow from the off-diagonal and off mass-shell mesonic T-matrix, with no contribution to the central charge. The construction is then extended to mesonic states on the light front, and shown to probe the moments of the partonic PDFs for large light-front separations. In the vacuum and for small and large intervals, the spatial entanglement entropy following from the Renyi entropy, is shown to be in agreement with the Ryu-Takayanagi geometrical entropy, using a soft-wall AdS$_3$ model of two-dimensional QCD.

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.

Hadronic structure on the light front. III. The Hamiltonian, heavy quarkonia, spin, and orbit mixing

This is the third paper on hadronic light-front wave functions. We derive a light-front Hamiltonian from first principles, using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes, and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schr\"odinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study spin-spin and spin-orbit mixing, resulting in e.g. quadrupole moments of vector mesons. For the light mesons, we show how to extend the famed 't Hooft interaction to the light front, which solves the U(1) problem and helps produce a light pion. We use the ensuing light front wave functions to derive the pertinent parton distribution functions, parton amplitudes, and low energy constants.

Hadronic structure on the light front. I. Instanton effects and quark-antiquark effective potentials

This is the first of a sequence of papers that addresses the nonperturbative origin of the central and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center-of-mass frame. We suggest a novel ``dense instanton ensemble'' model for the QCD vacuum, to explain the interquark forces in mesons, from quarkonia to heavy-light and light-light ones. The sequels will show how to export these interactions to the light front, and derive the corresponding Hamiltonians, mesonic, and baryonic light front wave functions. The ultimate aim of the series is to bridge the gap between hadronic spectroscopy and partonic observables.

Hadronic structure on the light front. IV. Heavy and light baryons

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front. The chief focus of this paper is the quantum-mechanical solution of the three-quark model Hamiltonian, describing baryons. In Jacobi coordinates, we use a harmonic oscillator basis for the transverse directions. For the longitudinal momentum fractions $x_i$, the pertinent basis follows from quantum mechanics in a "triangular cup" potential, which we solve exactly. We calculate the masses and light front wave functions for the flavor symmetric $\frac 32^+$ baryons $bbb,ccc,sss,uuu$.

Hadronic structure on the light front. V. Diquarks, nucleons, and multiquark Fock components

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. In this paper we focus on the importance of diquark correlations, which we describe by a quasi-local four-fermion effective 't Hooft interaction induced by instantons. The same interaction is also shown to generate extra quark-antiquark pair of the "sea". Its higher order iteration can be included via "pion-mediation": both taken together yield a quantitative description of the observed flavor asymmetry of antiquarks sea. Finally we discuss the final step needed to bridge the gap between hadronic spectroscopy and parton observables, by forward DGLAP evolution towards the chiral upper scale of $\sim 1\, {\rm GeV}^2$.

Light quark decays of doubly heavy baryons in light front approach

We explore the semileptonic and nonleptonic decays of doubly heavy baryons (Omega _{cc}^{(*)+},Omega _{bb}^{(*)0},Omega _{bc}^{(*)-},Omega _{bc}^{prime 0}) induced by the srightarrow u transition. Hadronic form factors are parametrized by transition matrix elements and are calculated in the light front quark model. With the form factors, we make use of helicity amplitudes and analyze semileptonic and nonleptonic decay modes of doubly heavy baryons. Benchmark results for partial decay widths, branching fractions, forward–backward asymmetries and other phenomenological observables are derived. We find that typical branching fractions for semileptonic decays into ell bar{nu } are at the order 10^{-7}-10^{-8} and the ones for nonleptonic decays are at the order 10^{-5}, which are likely detectable such as in LHCb experiment. With the potential data accumulated in future, our results may help to shape our understanding of the decay mechanism in the presence of two heavy quarks.

Mass decomposition of the pion in the ’t Hooft model

We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variational method and obtain numerical results for its energy breakdown into quark and gluon contributions.

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.

The averaging problem on the past null cone in inhomogeneous dust cosmologies

Cosmological models typically neglect the complicated nature of the spacetime manifold at small scales in order to hypothesize idealized general relativistic solutions for describing the average dynamics of the Universe. Although these solutions are remarkably successful in accounting for data, they introduce a number of puzzles in cosmology, and their foundational assumptions are therefore important to test. In this paper, we go beyond the usual assumptions in cosmology and propose a formalism for averaging the local general relativistic spacetime on an observer's past null cone: we formulate average properties of light fronts as they propagate from a cosmological emitter to an observer. The energy-momentum tensor is composed of an irrotational dust source and a cosmological constant -- the same components as in the $\Lambda$CDM model for late cosmic times -- but the metric solution is not \emph{a priori}constrained to be locally homogeneous or isotropic. This generally makes the large-scale dynamics depart from that of a simple Friedmann--Lema\^\i tre--Robertson--Walker solution through \emph{backreaction} effects. Our formalism quantifies such departures through a fully covariant system of area-averaged equations on the light fronts propagating towards an observer, which can be directly applied to analytical and numerical investigations of cosmic observables. For this purpose, we formulate light front averages of observable quantities, including the effective angular diameter distance and the cosmological redshift drift and we also discuss the backreaction effects for these observables.

Spatial densities of the photon on the light front

The light front densities of momentum, angular momentum, and intrinsic pressure are calculated for the photon, both in the free case and at leading order in quantum electrodynamics. In the latter case, we moreover decompose the form factors into photon and electron contributions. Circularly and linearly polarized photons are both considered, with the latter containing significant azimuthal modulations in both the momentum density and in intrinsic stresses. We find that the $D$-term of the photon is positive instead of negative, and accordingly the intrinsic radial pressure of the photon is negative. Despite this, the radiation pressure exerted by the photon is positive. We illustrate through explicit calculation how the intrinsic pressure associated with the $D$-term and the radiation pressure exerted by the photon are different quantities.

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.

Chiral sum rule on the light front and the 3D image of the pion

The lightest meson, the pion, features two faces – one is the elementary Goldstone boson of QCD and the other is the structured bound state of quarks and gluons. To accommodate both in a single light-front wave function in the valence space, we obtain a sum rule by analyzing the conserved axial-vector current and the general structures of the wave functions. Using an analytic model motivated by holography, we show this sum rule is consistent with requirements of chiral symmetry breaking in AdS/QCD. Within this model, we find a remarkable feature of the pion, namely that the density is mostly uniform inside its radius; furthermore, we obtain good agreement with the experimental pion form factor at spacelike momenta.

D* and Ds* distribution amplitudes from Bethe-Salpeter wave functions

We report on the first calculation of the longitudinal and transverse light front distribution amplitudes of the $D^*$ and $D^*_s$ mesons and their first four moments. As a byproduct, we also obtain these distribution amplitudes for the $\rho$, $\phi$, $K^*$ and $J/\Psi$ mesons and confirm a prediction of lattice QCD for the vector kaon: while the longitudinal distribution amplitude is almost symmetric, the transverse one is oblique implying that the strange quark carries more momentum.

Light Front Holographic QCD and Chiral Symmetry Breaking

Supersymmetric Light Front Holographic QCD is a holographic theory which exhibits typical features of a spontaneously broken chiral symmetry: The existence of a massless boson and different masses for vector and axial vector mesons. The reasons for the occurrence of these signatures both in LFHQCD and in standard methods is sketched and the differences are highlighted.

Scalar and vector one-loop massive tadpole light-front gauge Feynman integrals

Light-front gauge is the most popular one to work with fundamental interactions, due to its characteristic maximum kinematical Poincare operators that it allows. However, it is also known to be one of the trickiest gauges one can work with for gauge theories, due to its singular nature. So, in terms of perturbative calculations in the light-front, there are only a few published and tabulated results for the pertinent Feynman integrals, mostly involving massless integrals. And the majority of the results given are only for the divergent parts of them and the complete closed form (or with the finite parts) of these are not known. In this paper, we use the technique of negative dimensional integration for the simplest of the one-loop massive integrals as a working bench for massive Feynman integrals in the light front and show that novel results for the finite parts not known before are obtained.

Gravitational form factors and mechanical properties of the proton: Connections between distributions in 2D and 3D

The gravitational form factors which are obtained from the matrix elements of the energy-momentum tensor provide us information about internal distributions of mass, energy, pressure, and shear. The Druck term is the least understood among all the gravitational form factors. In a light front quark-diquark model of a proton, we investigate the Druck form factor. Using Abel transformation, we evaluate the 3D distribution in the Breit frame from the 2D light front distributions. The results are compared with other models and lattice predictions.