Light Front Research Articles

Genuine empirical pressure within the proton

A phenomenological extraction of pressure within the proton has recently been performed using JLab CLAS data (arXiv:2104.02031 [nucl-ex]). The extraction used a 3-dimensional Breit frame description in which the initial and final proton states have different momenta. Instead, we obtain the two-dimensional transverse light front pressure densities that incorporate relativistic effects arising from the boosts that cause the initial and final states to differ. The mechanical radius is then determined to be $0.518~ \pm 0.062_{\mathrm{fit}} \pm 0.126_{\mathrm{sys}}~\mathrm{fm}$, which is smaller than the electric charge radius and larger than the light front momentum radius. The forces within the proton are shown to be predominantly repulsive at distances less than $0.43~\pm 0.12~\mathrm{fm}$ from the center, and predominantly attractive further out.

Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case

We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. The beauty and simplicity of the Abel transformations allow us to derive a number of new relations for light front force distributions. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. Due to the positivity property of the Abel transformation we obtain an important result---the 2D local stability conditions are satisfied automatically if the corresponding 3D stability conditions are fulfilled. In this way we established not only mathematical equivalence of 2D and 3D forces distributions but also their physics equivalence in terms of stability. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large ${N}_{c}$ nucleon as a chiral soliton.

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.

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.

Exotic states in a holographic theory

Supersymmetric Light Front Holographic QCD is a holographic theory which predicts the existence of tetraquarks. The masses of those states, together with a discussion of its limitations are given.

Analisa Kerusakan Perkerasan Jalan Aspal

The road Kari Taluk Kuantan Terminal is a cross-road with flexible pavement that has suffered severe damage. The research objective was to find the remaining life of the pavement plan and the degree of damage to the asphalt pavement, using the Bina Marga method. During the service period, the pavement will experience repeated loading which causes damage, especially on the road section of the Terminal Kari Teluk Kuantan, Kuantan Singingi Regency STA 2 + 700 to 4 + 175. The results of the analysis that have been done, that: The remaining life of the pavement for the next 10 years = 12%, with a Truck Factor 0.465 <1, which means that the road is not fit to pass, The degree of damage for light front wheel vehicles is 0.0001, bus 0.0246, Truck 2 as 0.0178. The degree of damage for light vehicle rear wheels is 0.0001, buses 0.1245, Truck 2 as 0.0900, meaning that the average degree of damage for light vehicles and heavy vehicles, is less than one axis, in this case the damage is classified as collapse due to damage, with vehicle load normal which does not really affect the degree of damage to the road.

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.

Nonperturbative quark-antiquark interactions in mesonic form factors

The existing theory of hard exclusive QCD processes is based on two assumptions: (i) factorization into a hard block convoluted with the light front distribution amplitudes; (ii) use of perturbative gluon exchanges within the hard block. However, unlike deep inelastic scattering and jet physics, the characteristic momentum transfer $Q$ involved in the factorized block is not large enough for this theory to be phenomenologically successful. In this work, we revisit the latter assumption (ii), by explicitly calculating the instanton-induced contributions to the hard block, and show that they contribute substantially to the vector, scalar, and gravitational form factors of the pseudoscalar, scalar, and vector mesons, over a wide range of momentum transfer.

Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by random motion, while higher-order exponents grow by faster trajectories, such as ballistic excursions or "light fronts". Often such a situation is characterized by two linear dependencies of the exponents on their order. Here, we introduce a simple exactly solvable model, the Fly-and-Die (FnD) model, that sheds light on this behavior and on the consequences of light fronts on displacement autocorrelation functions in transport processes. We present analytical expressions for the moments and derive a scaling form that expresses the long-time asymptotics of the autocorrelation function $\langle x(t_1)\,x(t_2)\rangle$ in terms of the dimensionless time difference $(t_2-t_1)/t_1$. The scaling form provides a faithful collapse of numerical data for vastly different systems. This is demonstrated here for the Lorentz gas with infinite horizon, polygonal billiards with finite and infinite horizon, the L\'evy-Lorentz gas, the Slicer Map, and L\'evy walks. Our analysis also captures the system-specific corrections to scaling.

A numerical method of improved bandwidth adaptability for simulating diffraction integral of a spatial light modulator

In order to improve the adaptability of spatial light modulator diffraction analysis method to the research object, Collins–Huygens integral is introduced into spatial light modulator (SLM) diffraction analysis. This paper takes two kinds of hollow vortex light waves as examples to discuss the practicability of the simulation method. When the spatial light modulator is used to control the light wave front, the method can greatly improve the adaptability of various types of wave front as simulation objects. In particular, the diffraction of two different types of “holograms” is analyzed, one is CGH that produces hypergeometric beams with extremely wide spatial spectrum, and the other is CGH that produces Laguerre—Gaussian beams with limited spatial bandwidth. In this paper, the phase extraction method in numerical simulation calculation is discussed in detail, and the diffraction characteristics of phase mask and amplitude mask, such as missing order phenomenon, are verified by the numerical method in this paper. Through the simulation, we find that the method proposed in this paper is an effective simulation analysis method. Its applications range from generating light beams with angular momentum to microscopes to trapping neutral atoms. The method is also extended to other beam shaping components using SLM.

Observing the Minkowskian dynamics of the pion on the null-plane

A dynamical model is applied to the study of the pion valence light-front wave function, obtained from the actual solution of the Bethe-Salpeter equation in Minkowski space, resorting to the Nakanishi integral representation. The kernel is simplified to a ladder approximation containing constituent quarks, an effective massive gluon exchange, and the scale of the extended quark-gluon interaction vertex. These three input parameters carry the infrared scale {\Lambda}QCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides f{\pi}, we present and discuss other interesting quantities on the null-plane, like: (i) the valence probability, (ii) the dynamical functions depending upon the longitudinal or the transverse components of the light-front (LF) momentum, represented by LF-momentum distributions and distribution amplitudes, and (iii) the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates, in order to perform an analysis of the dynamical features in a complementary way. The proposed analysis of the Minkowskian dynamics inside the pion, though carried out at the initial stage, qualifies the Nakanishi integral representation as an appealing effective tool, with still unexplored potentialities to be exploited for addressing correlations between dynamics and observable properties.

Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tagging

Background: DIS on the polarized deuteron with detection of a proton in the nuclear breakup region (spectator tagging) represents a unique method for extracting the neutron spin structure functions and studying nuclear modifications. The tagged proton momentum controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. Such measurements could be performed with the future electron-ion collider (EIC) and forward proton detectors if deuteron beam polarization could be achieved. Purpose: Develop theoretical framework for polarized deuteron DIS with spectator tagging. Formulate procedures for neutron spin structure extraction. Methods: A covariant spin density matrix formalism is used to describe general deuteron polarization in collider experiments (vector/tensor, pure/mixed). Light-front (LF) quantum mechanics is employed to factorize nuclear and nucleonic structure in the DIS process. A 4-dimensional representation of LF spin structure is used to construct the polarized deuteron LF wave function and efficiently evaluate the spin sums. Free neutron structure is extracted using the impulse approximation and analyticity in the tagged proton momentum (pole extrapolation). Results: General expressions of the polarized tagged DIS observables in collider experiments. Analytic and numerical study of the polarized deuteron LF spectral function and nucleon momentum distributions. Practical procedures for neutron spin structure extraction from the tagged deuteron spin asymmetries. Conclusions: Spectator tagging provides new tools for precise neutron spin structure measurements. D-wave depolarization and nuclear binding effects can be eliminated through the tagged proton momentum dependence. The methods can be extended to tensor-polarized observables, spin-orbit effects, and diffractive processes.

Vacuum loops in light-front field theory

We demonstrate that vacuum diagrams in the genuine light front (LF) field theory are non-zero, in spite of simple kinematical counter-arguments (positivity and conservation of the LF momentum p+, absence of Fourier zero mode). Using the light-front Hamiltonian (time-ordered) perturbation theory, the vacuum amplitudes in self-interacting scalar λϕ3(1+1) and λϕ4(1+1) models are obtained as p=0 limit of the associated self-energy diagrams, where p is the external momentum. They behave as Cλ2μ−2 in D=2, with μ being the scalar-field mass, or diverge in D=4, in agreement with the usual “equal-time” form of field theory, and with the same value of the constant C. The simplest vacuum diagram with two internal lines is analyzed in detail displaying the subtle role of the small k+ region and its connection to the p=0 limit. However, the vacuum bubbles in the genuine light-front field theory are nonvanishing not due to the Fourier mode carrying LF momentum k+=0 (as is the case in the LF evaluation of the covariant Feynman diagrams), in full accord with the observation that the LF perturbation theory formula breaks down in the exact zero-mode case. This is made explicit using the DLCQ method - the discretized (finite-volume) version of the theory, where the light-front zero modes are manifestly absent, but the vacuum amplitudes still converge to their continuum-theory values with the increasing “harmonic resolution” K.

Scalar spectrum in a graviton soft wall model

In this study we present a unified phenomenological analysis of the scalar glueball and scalar meson spectra within an AdS/QCD framework in the bottom up approach. For this purpose we generalize the recently developed graviton soft-wall (GSW) model, which has shown an excellent agreement with the lattice QCD glueball spectrum, to a description of glueballs and mesons with a unique energy scale. In this scheme, dilatonic effects, are incorporated in the metric as a deformation of the AdS space. We apply the model also to the heavy meson spectra with success. We obtain quadratic mass equations for all scalar mesons while the glueballs satisfy an almost linear mass equation. Besides their spectra, we also discuss the mixing of scalar glueball and light scalar meson states within a unified framework: the GSW model. To this aim, the light-front (LF) holographic approach, which connects the mode functions of AdS/QCD to the LF wave functions, is applied. This relation provides the probabilistic interpretation required to properly investigate the mixing conditions.

High-efficiency broadband photonic crystal fiber metalens with a large numerical aperture

Photonic Crystal Fiber (PCF), as a novel optical fiber, is widely used in the applications of dispersion control, supercontinuum generation, fiber sensing, etc. However, the numerical aperture (NA) of most PCFs is normally too low to obtain a high coupling efficiency, and the transmitted light is easy to diverge, which limited the applications of PCFs. In recent years, the rapid development of metasurface optics provided an unparalleled platform for improving the optical properties and functionality of the PCFs. Here, we designed two PCF devices integrated with the metalens operating in the telecom region on the basis of numerical simulation, namely PCF divergent metalens (PCF-DM) and PCF focusing metalens (PCF-FM). The simulation results demonstrated that the proposed devices can increase the NA of a PCF from less than 0.1 to 0.65 with coupling efficiencies as high as 90% and 85% through shaping the wave front of the incident light. Meanwhile, it is found that PCF-FM can enhance the focusing capability of a PCF and leads to a focus with a size near the diffraction limit, moreover maintaining a high focusing efficiency. Therefore, we anticipate that the reported novel design would contribute to researches of fiber imaging/sensing, fiber laser, and other PCF-based devices.

Distribution amplitudes of heavy mesons and quarkonia on the light front

The ladder kernel of the Bethe–Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the D_u, D_s, B_u, B_s and B_c mesons and the heavy quarkonia eta _c and eta _b within the same framework at a physical pion mass. The corresponding Bethe–Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.

Relativistic corrections to the vector meson light front wave function

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.

Two-body light front wave functions from general AdS/QCD models

In this work, we consider 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 compute the light-front wave function (LFWF) considering different static dilaton fields and AdS-like geometric deformations. We also prove that this procedure holds for general AdS/QCD models in asymptotically AdS geometries.

Parton distribution functions of heavy mesons on the light front

The parton distribution functions (PDFs) of heavy mesons are evaluated from their light-front wave functions, which are obtained from a basis light-front quantization in the leading Fock sector representation. We consider the mass eigenstates from an effective Hamiltonian consisting of the confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with running coupling. We present the gluon and the sea quark PDFs which we generate dynamically from the QCD evolution of the valence quark distributions.

Hadroproduction of scalar P -wave quarkonia in the light-front kT -factorization approach

In this work, we present a thorough analysis of scalar P -wave χQ0, Q = c, b quarkonia electromagnetic form factors for the γ∗γ∗→ χQ0 couplings, as well as their hadroproduction observables in k⊥-factorisation using the light-front (LF) potential approach for the quarkonium wave function. The electromagnetic form factors are presented as functions of photon virtualities. We discuss the role of the Melosh spin-rotation and relativistic corrections estimated by comparing our results with those in the standard nonrelativistic QCD (NRQCD) approach. Theoretical uncertainties of our approach are found by performing the analysis with two different unintegrated gluon densities and with five distinct models of the Qoverline{Q} interaction potentials consistent with the meson spectra. The results for the rapidity and transverse momentum distributions of χQ0 produced in high-energy pp collisions at sqrt{s} = 13 TeV are shown.