Light-front Dynamics Research Articles

Light-front model for the transition distribution amplitudes for backward timelike Compton scattering

To access information on the internal structure of the nucleon, data from a variety of scattering experiments can be analyzed in regimes where the information factorizes from an otherwise known scattering amplitude. A recent development, promising new insight, is the study of exclusive reactions in the backward kinematical region, where the information can be encoded in transition distribution amplitudes. We model the photon-to-nucleon transition distribution amplitudes, entering the factorized description of backward timelike Compton scattering, using techniques of light-front dynamics to integrate information from a quark model for the photon and the nucleon. We include the results of numerical predictions that could inform further experiments at Jefferson Lab and the future Electron-Ion Collider. Published by the American Physical Society 2024

Quantum electrodynamics in the null-plane causal perturbation theory. II.

We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to quantum electrodynamics, showing that the so-called "gauge terms" present in the photon commutation distribution when quantized under the null-plane gauge condition have no contribution in the calculation of the physical S-operator matrix elements at any order. We use this result to prove the normalizability of the theory, and to calculate the electron's self-energy at second order.

The pion in the graviton soft-wall model: phenomenological applications

The holographic graviton soft-wall model, introduced to describe the spectrum of scalar and tensor glueballs, is improved to incorporate the realization of chiral-symmetry as in QCD. Such a goal is achieved by including the longitudinal dynamics of QCD into the scheme. Using the relation between AdS/QCD and light-front dynamics, we construct the appropriate wave function for the pion which is used to calculate several pion observables. The comparison of our results with phenomenology is remarkably successful.

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.

Proton image and momentum distributions from light-front dynamics

We apply a dynamical three-constituent quark light-front model to study the proton. The dynamics is based on the notion of a diquark (bound or virtual) as the dominant interaction channel, which paramaterizes a contact interaction between the quarks in order to build the three-body Faddeev Bethe-Salpeter equations for the valence state, and we focus on the totally symmetric part of the wave function. The Dirac electromagnetic form factor is used to fix the model parameters, and the valence wave function is obtained. From that we investigate its Ioffe-time image, non-polarized longitudinal and transverse momentum distributions, and the double momentum distribution.

Interpolating ’t Hooft model between instant and front forms

The 't Hooft model, i.e., the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $\ensuremath{\delta}$ between $\ensuremath{\delta}=0$ for the instant form dynamics (IFD) and $\ensuremath{\delta}=\ensuremath{\pi}/4$ for the light-front dynamics (LFD). With this parameter $\ensuremath{\delta}$, we formulate the interpolating mass gap equation which takes into account the nontrivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions not only reproduce the previous IFD result at $\ensuremath{\delta}=0$ as well as the previous LFD result at $\ensuremath{\delta}=\ensuremath{\pi}/4$ but also link them together between the IFD and LFD results with the $\ensuremath{\delta}$ parameter. We find the interpolation angle independent characteristic energy function which satisfies the energy-momentum dispersion relation of the dressed fermion, identifying the renormalized fermion mass function and the wave function renormalization factor. The renormalized fermion condensate is also found independent of $\ensuremath{\delta}$, indicating the persistence of the nontrivial vacuum structure even in the LFD. Using the dressed fermion propagator interpolating between IFD and LFD, we derive the corresponding quark-antiquark bound-state equation in the interpolating formulation verifying its agreement with the previous bound-state equations in the IFD and LFD at $\ensuremath{\delta}=0$ and $\ensuremath{\delta}=\ensuremath{\pi}/4$, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the $\ensuremath{\delta}$-parameter reproducing the previous results in LFD and IFD for the equal mass quark and antiquark bound states. The Gell-Mann-Oakes-Renner relation for the pionic ground-state in the zero fermion mass limit is confirmed indicating that the spontaneous breaking of the chiral symmetry occurs in the 't Hooft model regardless of the quantization for $0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}\ensuremath{\pi}/4$. We obtain the corresponding bound-state wave functions and discuss their reference frame dependence with respect to the frame independent LFD result. Applying them for the computation of the so-called quasi-parton distribution functions now in the interpolating formulation between IFD and LFD, we note a possibility of utilizing not only the reference frame dependence but also the interpolation angle dependence to get an alternative effective approach to the LFD-like results.

Radiative corrections in the Yukawa model within the null-plane causal perturbation theory framework

Practical calculations in light-front dynamics are, as a general rule, complicated, since there is no consensus about how to treat the poles which come from the instantaneous parts of Feynman's propagators of the fields. An alternative to solve this difficulty is null-plane causal perturbation theory, a recent developed framework which prevents the appearance of the mentioned poles by avoiding the usage of Feynman's propagators in ``loop distributions,'' requiring no regularization of the amplitudes. In this study, we treat the radiative corrections in the neutral Yukawa's model in that framework. Particularly, we explicitly calculate the boson and fermion self-energies and show that the results obtained with this approach are equivalent to that of the instant dynamics.

Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in ( 1+1 ) dimensions

We investigate the electromagnetic form factor $F(q^2)$ of the meson by using the solvable $\phi^{3}$ scalar field model in $(1+1)$ dimensions. As the transverse rotations are absent in $(1+1)$ dimensions, the advantage of the light-front dynamics (LFD) with the light-front time $x^+ = x^0 + x^3$ as the evolution parameter is maximized in contrast to the usual instant form dynamics (IFD) with the ordinary time $x^0$ as the evolution parameter. In LFD, the individual $x^+$-ordered amplitudes contributing to $F(q^2)$ are invariant under the boost, i.e., frame-independent, while the individual $x^0$-ordered amplitudes in IFD are not invariant under the boost but dependent on the reference frame. The LFD allows to get the analytic result for the one-loop triangle diagram which covers not only the spacelike ($q^{2}<0$) but also timelike region ($q^{2}>0$). Using the analytic results, we verify that the real and imaginary parts of the form factor satisfy the dispersion relations in the entire $q^{2}$ space. Comparing with the results in $(3+1)$ dimensions, we discuss the transverse momentum effects on $F(q^2)$ . We also discuss the longitudinal charge density in terms of the boost invariant variable $\tilde z = p^+ x^-$ in LFD.

Hybrid nature of the abnormal solutions of the Bethe\u2013Salpeter equation in the Wick\u2013Cutkosky model

In the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called “normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.

Short-Range NN Correlations in the Reaction 12C + p → 10A + pp + N

The exclusive reaction 12C(p,pNN)10A of the quasi-elastic knockout of a nucleon from short-range correlated nucleon pair $$\langle NN\rangle $$ in the 12С nucleus by a proton with an energy of several gigaelectronvolts is considered in the plane-wave approximation. The translational invariant shell model with intermediate coupling is used to calculate two-nucleon spectroscopic factors for the $$\langle NN\rangle $$ pairs. Relativistic effects in the p + $$\langle NN\rangle $$ → p + N + N process are considered within light front dynamics.

Pauli\u2013Villars regularization elucidated in Bopp\u2013Podolsky\u2019s generalized electrodynamics

We discuss an inherent Pauli–Villars regularization in Bopp–Podolsky’s generalized electrodynamics. Introducing gauge-fixing terms for Bopp–Podolsky’s generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli–Villars regularization independent of the gauge choice made in Maxwell’s usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp–Podolsky’s higher order derivatives corresponds to the inverse of the Pauli–Villars regularization mass scale Lambda , i.e. a = 1/Lambda . Solving explicitly the classical static Bopp–Podolsky’s equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics.

Frame dependence of transition form factors in light-front dynamics

We calculate the transition form factor between vector and pseudoscalar quarkonia in both the timelike and the spacelike region using light-front dynamics. We investigate the frame dependence of the form factors for heavy quarkonia with light-front wavefunctions calculated from the valence Fock sector. This dependence could serve as a measure for the Lorentz symmetry violation arising from the Fock-space truncation. We suggest using frames with minimal longitudinal momentum transfer for calculations in the valence Fock sector, namely the Drell-Yan frame for the space-like region and a specific longitudinal frame for the timelike region; at $q^2=0$ these two frames give the same result. We also use the transition form factor in the timelike region to investigate the electromagnetic Dalitz decay $\psi_A\to \psi_B l^+l^-$ ($l = e,\mu$) and predict the effective mass spectrum of the lepton pair.

Defining the proton radius: A unified treatment

Background: There is significant current interest in knowing the value of the proton radius and also its proper definition. Purpose: Combine the disparate literatures of hydrogen spectroscopy and diverse modern parton distributions to show that the quantity $r_p^2\equiv -6 G_E'(0)$ is the relativistically proper definition that originates from the separate bodies of work. Methods: Use perturbation theory, light-front dynamics and elementary techniques to find relativistically correct definitions of the proton radius and charge density. Results: It is found that the very same proton radius is accessed by measurements of hydrogen spectroscopy and elastic lepton scattering. The derivation of the mean-square radius as a moment of a spherically symmetric three-dimensional density is shown to be incorrect. A relativistically-correct, two-dimensional charge density is related to the diverse modern literature of various parton distributions. Relativistically invariant moments thereof are derived in a new moment expansion, the RME.

Supersymmetric and Conformal Features of Hadron Physics

The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion q q ¯ eigenstate has zero mass for m q = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α s ( Q 2 ) ∝ e − Q 2 / 4 κ 2 , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

Interpolating quantum electrodynamics between instant and front forms

The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $\delta$ spanning between the instant form dynamics (IFD) at $\delta =0$ and the front form dynamics which is now known as the light-front dynamics (LFD) at $\delta =\pi/4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed in our previous work, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as $e^+ e^- \to \gamma \gamma$ and $e \gamma \to e \gamma$ and present the whole landscape of the scattering amplitudes in terms of the frame dependence or the scattering angle dependence with respect to the interpolating angle dependence. Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame approach and the LFD.

Supersymmetry in the double-heavy hadronic spectrum

Relativistic light-front bound-state equations for double-heavy mesons, baryons and tetraquarks are constructed in the framework of supersymmetric light front holographic QCD. Although heavy quark masses strongly break conformal symmetry, supersymmetry and the holographic embedding of semiclassical light-front dynamics still holds. The theory, derived from five-dimensional anti-de Sitter space, predicts that the form of the confining potential in the light-front Hamiltonian is harmonic even for heavy quarks. Therefore, the basic underlying supersymmetric mechanism, which transforms meson-baryon and baryon-tetraquark wave functions into each other, can also be applied to the double-heavy sector; one can then successfully relate the masses of the double-heavy mesons to double-heavy baryons and tetraquarks. The dependence of the confining potential on the hadron mass scale agrees completely with the one derived in heavy light systems from heavy quark symmetry. We also make predictions for higher excitations of the charmonium and bottomonium states. In particular, the remarkable equality of the Regge slopes in the orbital angular momentum, $L$, and the principal quantum number, $n$, is predicted to remain valid.

Interpolating Quantum Electrodynamics

We discuss the interpolation between the instant form dynamics (IFD) and the light-front dynamics (LFD) proposed by Dirac in 1949 and present its application to quantum electrodynamics (QED). Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the IFD at infinite momentum frame and the LFD. Entwining the fermion propagator interpolation with our previous works of the interpolating helicity spinors and the electromagnetic gauge field interpolation, we fasten the bolts and nuts necessary to launch the interpolating QED at least in the tree level.

Spin-1 Particles and Perturbative QCD

Due to the angular condition in the light-front dynamics (LFD), the extraction of the electromagnetic form factors for spin-1 particles can be uniquely determined taking into account implicitly non-valence and/or the zero-mode contributions to the matrix elements of the electromagnetic current. No matter which matrix elements of the electromagnetic current is used to extract the electromagnetic form factors, the same unique result is obtained. As physical observables, the electromagnetic form factors obtained from matrix elements of the current in LFD must be equal to those obtained in the instant form calculations. Recently, the Babar collaboration \cite{Aubert2008} has analyzed the reaction $e^+ e^-\rightarrow \rho^+ + \rho^-$ at $\sqrt{s}=10.58 GeV$ to measure the cross section as well as the ratios of the helicity amplitudes $F_{\lambda'\lambda}$. We present our recent analysis of the Babar data for the rho meson considering the angular condition in LFD to put a stringent test on the onset of asymptotic perturbative QCD and predict the energy regime where the subleading contributions are still considerable.

Frame dependence of form factors in light-front dynamics

In light-front dynamics, form factors are traditionally computed with the "good current" $J^+$ within the Drell-Yan frame $q^+=0$. Due to truncations imposed in practical calculations, the from factor may acquire frame dependence, which is often neglected. In this work, we explore the form factors in more general frames, preserving the boost covariance. We find the frame dependence of the elastic form factors for mesons is small in basis light-front holography and related models with two-body Fock space truncation. We suggest to use the difference between form factor results from Drell-Yan frame and the "longitudinal frame" as a metric for the violation of the Lorentz symmetry due to Fock space truncation.

Three–Dimensional parton structure of light nuclei

Two promising directions beyond inclusive deep inelastic scattering experiments, aimed at unveiling the three dimensional structure of the bound nucleon, are reviewed, considering in particular the 3He nuclear target. The 3D structure in coordinate space can be accessed through deep exclusive processes, whose non-perturbative part is encoded in generalized parton distributions. In this way, the distribution of partons in the transverse plane can be obtained. As an example of a deep exclusive process, coherent deeply virtual Compton scattering off 3He nuclei, important to access the neutron generalized parton distributions (GPDs), will be discussed. In Impulse Approximation (IA), the sum of the two leading twist, quark helicity conserving GPDs of 3He, H and E, at low momentum transfer, turns out to be dominated by the neutron contribution. Besides, a technique, able to take into account the nuclear effects included in the Impulse Approximation analysis, has been developed. The spin dependent GPD of 3He is also found to be largely dominated, at low momentum transfer, by the neutron contribution. The knowledge of the GPDs H,E and of 3He is relevant for the planning of coherent DVCS off 3He measurements. Semi-inclusive deep inelastic scattering processes access the momentum space 3D structure parameterized through transverse momentum dependent parton distributions. A distorted spin-dependent spectral function has been recently introduced for 3He, in a non-relativistic framework, to take care of the final state interaction between the observed pion and the remnant in semi-inclusive deep inelastic electron scattering off transversely polarized 3He. The calculation of the Sivers and Collins single spin asymmetries for 3He, and a straightforward procedure to effectively take into account nuclear dynamics and final state interactions, will be reviewed. The Light-front dynamics generalization of the analysis is also addressed.