Light Front Research Articles

The Light-Front Schrödinger Equation and the Determination of the Perturbative QCD Scale from Color Confinement: A First Approximation to QCD

The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$ has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number $n$ and orbital angular momentum $L$. Only one mass parameter $\kappa$ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale $\kappa$ underlying confinement and hadron masses determines the scale $\Lambda_{\overline{MS}} $ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value $\Lambda_{\overline{MS}} = 0.328 \pm 0.034$ GeV is in agreement with the world average $0.339 \pm 0.010$ GeV. The analysis applies to any renormalization scheme.

Engineering the phase front of light with phase-change material based planar lenses.

A novel hybrid planar lens is proposed to engineer the far-field focusing patterns. It consists of an array of slits which are filled with phase-change material Ge2Sb2Te5 (GST). By varying the crystallization level of GST from 0% to 90%, the Fabry-Pérot resonance supported inside each slit can be spectrally shifted across the working wavelength at 1.55 µm, which results in a transmitted electromagnetic phase modulation as large as 0.56π. Based on this geometrically fixed platform, different phase fronts can be constructed spatially on the lens plane by assigning the designed GST crystallization levels to the corresponding slits, achieving various far-field focusing patterns. The present work offers a promising route to realize tunable nanophotonic components, which can be used in optical circuits and imaging applications.

Modern studies of the Deuteron: From the lab frame to the light front

We review the recent progress made in studies of deuteron structure at small internucleon distances. This progress is largely facilitated by the new generation of experiments in deuteron electrodisintegration carried out at unprecedentedly high momentum transfer. The theoretical analysis of these data confirms the onset of the high energy eikonal regime in the scattering process which allows one to separate long-range nuclear effects from the effects genuinely related to the short distance structure of the deuteron. Our conclusion is that for the first time the deuteron is probed at relative momenta beyond 300 MeV/c without dominating long-range effects. As a result, at these large nucleon momenta the cross-section is sensitive to the nuclear dynamics at subfermi distances. Due to large internal momenta involved we are dealing with the relativistic bound state that is best described by the light-cone momentum distribution of nucleons in the deuteron. We present the first attempt of extracting the deuteron light-cone momentum distribution function from data and discuss the importance of this quantity for studies of quantum chromodynamics (QCD) structure of the bound nucleon in deep inelastic scattering (DIS) off the deuteron. We conclude the review giving an outlook of the next generation of high energy experiments which will extend our reach to much smaller distances in the deuteron.

Baryon spectrum from superconformal quantum mechanics and its light-front holographic embedding

We describe the observed light-baryon spectrum by extending superconformal quantum mechanics to the light front and its embedding in AdS space. This procedure uniquely determines the confinement potential for arbitrary half-integer spin. To this end, we show that fermionic wave equations in AdS space are dual to light-front supersymmetric quantum mechanical bound-state equations in physical space-time. The specific breaking of conformal invariance explains hadronic properties common to light mesons and baryons, such as the observed mass pattern in the radial and orbital excitations, from the spectrum generating algebra. The holographic embedding in AdS also explains distinctive and systematic features, such as the spin-$J$ degeneracy for states with the same orbital angular momentum, observed in the light baryon spectrum.

Spin Structure of the Nucleon on the Light Front

We briefly review the spin structure of the nucleon and show that it is best thought in the light-front formulation. We discuss in particular the longitudinal and transverse spin sum rules, the proper definition of canonical orbital angular momentum and the spin-orbit correlation.

Transverse distortion of a relativistic composite system in impact parameter space

We investigate the Generalized Parton Distributions (GPDs) in impact parameter space using the explicit light front wave functions (LFWFs) for the two-particle Fock state of the electron in QED. The Fourier transform (FT) of the GPDs gives the distribution of quarks in the transverse plane for zero longitudinal momentum transfer ($\xi=0$). We study the relationship of the spin flip GPD $E(x,0,-\vec{\Delta}_\perp^2)$ with the distortion of unpolarized quark distribution in the transverse plane when the target nucleon is transversely polarized and also determine the sign of distortion from the sign of anomalous magnetic moment. To verify the sign of distortion, we also compute it directly from the LFWFs by performing a FT in position space coordinate $\vec{f}_\perp$. The explicit relation between the deformation in the two spaces can also be obtained using the convolution integrals. To show the relation of the model LFWFs to a realistic model of nucleon physics, we have designed a specific weight function of our model LFWFs and integrated it over the mass parameter. Also we have simulated the form factor of the nucleon in the AdS/QCD holographic LFWFs model and studied the power-law behaviour at short distances.

Generalized Parton Distributions of proton for nonzero skewness in transverse and longitudinal position spaces

We investigate the Generalized Parton Distributions (GPDs) of proton by expressing them in terms of overlaps of light front wave functions (LFWFs) using a simulated model which is able to qualitatively improve the convergence near the end points of x. We study the spin nonflip H(x, ζ, t) and spin flip E(x, ζ, t) parts of GPDs for the particle conserving n → n overlap in the DGLAP region (ζ < x < 1). The Fourier transform (FT) of the GPDs with respect to the transverse momentum transfer as well as the FT of the GPDs with respect to ζ has also been obtained by giving the distribution of partons in the transverse position space and the distribution in the longitudinal position space, respectively. Diffraction pattern is obtained for both [Formula: see text] and [Formula: see text] in the longitudinal position space.

The Higgs oscillator on the hyperbolic plane and light-front holography

The Light Front Holographic (LFH) wave equation, which is the conformal scalar equation on the plane, is revisited from the perspective of the supersymmetric quantum mechanics, and attention is drawn to the fact that it naturally emerges in the small hyperbolic angle approximation to the "curved" Higgs oscillator on the hyperbolic plane, i.e. on the upper part of the two-dimensional hyperboloid of two sheets, a space of constant negative curvature. Such occurs because the particle dynamics under consideration reduces to the one dimensional Schr\"odinger equation with the second hyperbolic P\"oschl-Teller potential, whose flat-space (small-angle) limit reduces to the conformally invariant inverse square distance plus harmonic oscillator interaction, on which LFH is based. In consequence, energies and wave functions of the LFH spectrum can be approached by the solutions of the Higgs oscillator on the hyperbolic plane in employing its curvature and the potential strength as fitting parameters. Also the proton electric charge form factor is well reproduced within this scheme by means of a Fourier-Helgason hyperbolic wave transform of the charge density. In conclusion, in the small angle approximation, the Higgs oscillator on the hyperbolic plane is demonstrated to satisfactory parallel essential outcomes of the Light Front Holographic QCD. The findings are suggestive of associating the hyperboloid curvature of the with a second scale in LFH, which then could be employed in the definition of a chemical potential.

Light-Front Quantization with Explicit Lorentz Symmetry for Yukawa Model

The Dirac method for constrained systems is incomplete for the light-front (LF) quantization of the Yukawa model in D = 1 + 1 dimensions. A novel quantization procedure is proposed, where one obtains the LF commutator and anti-commutators directly from the Heisenberg equations generated by P+, which is a kinematical operator. By adding the general assumptions on the quantum field theory, one evalutes 2-point Wightman functions for a free field case. The Lorentz symmetry is manifest at every step of this novel LF procedure. The Gaussian effective potential is defined with the point-splitting regularization with a space-like separation. The optimum values of the mass parameters are regularization independent.

Application of Coherent State Approach for the Cancellation of Infrared Divergences to All Orders in LFQED

We sketch an all order proof of cancellation of infrared (IR) divergences in Light Front Quantum Electrodynamics (LFQED) using a coherent state formalism. In this talk, it has been shown that the true IR divergences in fermion self energy are eliminated to all orders in a light-front time-ordered perturbative calculation if one uses coherent state basis instead of the usual Fock basis to calculate the Hamiltonian matrix elements.

Double parton correlations and constituent quark models: a light front approach to the valence sector

An explicit evaluation of the double parton distribution functions (dPDFs), within a relativistic Light-Front approach to constituent quark models, is presented. dPDFs encode information on the correlations between two partons inside a target and represent the non-perturbative QCD ingredient for the description of double parton scattering in proton-proton collisions, a crucial issue in the search of new Physics at the LHC. Valence dPDFs are evaluated at the low scale of the model and the perturbative scale of the experiments is reached by means of QCD evolution. The present results show that the strong correlation effects present at the scale of the model are still sizable, in the valence region, at the experimental scale. At the low values of x presently studied at the LHC the correlations become less relevant, although they are still important for the spin-dependent contributions to unpolarized proton scattering.

Charge and magnetization densities in transverse coordinate and impact parameter space

Electromagnetic form factors obtained from the overlap of light front wave functions (LFWFs) have been used to study the transverse densities of charge and magnetization. The calculations have been carried out to develop a relation between the charge distribution of the quarks inside nucleon in the transverse coordinate space as well as in the impact parameter space. When a comparison is carried out, it is found that the transverse distribution in the impact parameter space, where the longitudinal momentum fraction $x$ can be fixed, falls off faster than the spatial distribution in the transverse coordinate space where there is some contribution from the longitudinal momentum as well. The anomalous magnetization density of the nucleon has also been discussed. Further, we have also presented the results of the QCD transverse AdS charge density inspired from the holographic QCD model.

Nucleonic helicity distributions revisited with an emphasis on their evolutions and twists

In this work, we uphold and extend the formalism advocated by us more than a decade ago in order to extract information on various distribution functions describing nucleonic helicity structure and calculate a complete set of splitting functions relevant for their quantum chromodynamics (QCD) evolutions using light-front Hamiltonian perturbation theory in light front gauge A + = 0. Twist-two structures of the helicity distributions are self-evident in our calculation. Sum rules associated with these helicity distributions are also verified in a frame-independent way.

Numerical analysis of the production ofD(*)(3000),DsJ(3040)and their partners through the semileptonic decays ofB(s)mesons in terms of the light front quark model

Inspired by the newly observed $D^{(*)}(3000)$, and $D_{sJ}(3040)$ states, in this work we study the production of $D^{(*)}(3000)$, $D_{sJ}(3040)$ and their partners through the semileptonic decays of $B_{(s)}$ mesons, where the light-front Quark model is applied to the whole calculation. Our numerical results indicate that the $B_{(s)}$ semileptonic decays into the $2P$ states of the charmed or charmed-strange meson family have considerable branching ratios, which shows that these semileptonic decays can be accessible at future experiments, especially LHCb and the forthcoming Belle II.

The application of light front holographic QCD to B physics

Light front holography is a formalism developed by Brodsky and de Téramond in which analytic forms for the hadronic bound state wavefunctions can be obtained. We have used the holographic light front wavefunctions thus obtained to calculate the distribution amplitudes of the light vector mesons ρ and K∗. As a result, we are able to calculate the form factors for B → ρ, K∗ transitions as well as ΛQCD/mb contributions in radiative B(s) → (ρ, K∗)γ decays. We compare our predictions to the available experimental data.

Zero Mode Effect Generalization for the Electromagnetic Current in the Light Front: Fermion Case

We investigate the effect of the γ+ term in the fermion propagator on the zero mode in a system composed of two free fermions propagating in a background field. For this purpose we use the technique of global propagators in the light front and current operator in order to obtain the electromagnetic current component J−.

Transfer-printed silver nanodisks for plasmonic light trapping in hydrogenated microcrystalline silicon solar cells

Plasmonic light trapping is a topic of high interest, but research regarding this topic has been so far impeded owing to the lack of convenient methods to produce desired metal nanostructures in solar cells. To overcome this challenge, we herein introduced a transfer printing approach and performed demonstrative light trapping. Promising results were verified with superstrate-type hydrogenated microcrystalline Si cells fabricated on flat superstrates; for example, the photocurrent generated in the 650–1100 nm range increased to up to 60%. Since our transfer printing approach was applicable to textured surfaces, the integration of plasmon-mediated light trapping and front texture-mediated light trapping was also explored.

Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization

We address the problem of nonperturbative calculations on the light front in quantum field theory regularized by Pauli-Villars method. As a preliminary step we construct light front Hamiltonians in (2+1)-dimensional λ φ 4 model, for the cases without and with spontaneous symmetry breaking. The renormalization of these Hamiltonians in Pauli-Villars regularization is carried out via comparison of all-order perturbation theory, generated by these Hamiltonians, and the corresponding covariant perturbation theory in Lorentz coordinates.

Self Energy Correction in Light Front QED And Coherent State Basis

We discuss the calculation of fermion self energy correction in Light Front QED using a coherent state basis. We show that if one uses coherent state basis instead of fock basis to calculate the transition matrix elements, the true infrared divergences in electron mass renormalization δm2 get canceled up to O(e4) in Light Front gauge. We have also verified this cancellation in Feynman gauge up to O(e2).

DSE Perspective on QCD Modeling, Distribution Amplitudes, and Form Factors

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale $\mu=~$2GeV by projecting the Poincar\'e-covariant Bethe-Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, $F_\pi(Q^2)$, on the entire domain of spacelike $Q^2$. The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking (DCSB) on the light front. We investigate the transition region of $Q^2$ where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson-Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for $Q^2 F_\pi(Q^2)$ underestimates the new DSE computation by just 15\% on $Q^2\gtrsim 8\,$GeV$^2$, in stark contrast with the result obtained using the asymptotic PDA.