Light-front Wave Functions Research Articles

Heavy flavor-asymmetric pseudoscalar mesons on the light front

We extract the leading Fock-state light front wave functions of heavy flavor-asymmetric pseudoscalar mesons D, B, and Bc from their Bethe-Salpeter wave functions, based on the Dyson-Schwinger equations approach. We then study their leading-twist parton distribution amplitudes, generalized parton distribution functions, and transverse momentum-dependent parton distributions. The spatial distributions of the quark and antiquark on the transverse plane are presented, along with their charge and energy distributions on the light front. We find that in the considered mesons, the heavier quarks carry most of the longitudinal momentum fraction, resulting in narrow x distributions, while the lighter quarks play an active role in shaping the transverse distributions in both spatial and momentum space, exhibiting a duality that embodies characteristics of both light mesons and heavy quarkonium. Published by the American Physical Society 2024

Spectroscopy of excited quarkonium states in the light-front quark model

Abstract We have investigated the ground state ($1S$), radially excited states ($2S$) and ($3S$) along with the orbitally excited state ($1P$) for the heavy charmonia ($c \bar c$) and bottomonia ($b \bar b$) mesons in the light-front quark model (LFQM). The light-front wave functions have been successful in explaining various physical properties of meson states in the past, especially for the $1S$ and $2S$ states. However, studies regarding the radially excited state $3S$ and orbitally excited state $1P$ have hardly been pursued before. In this study, we take up these two excited states and investigate the electromagnetic form factors (EMFFs), charge radii, decay constants, parton distribution functions (PDFs) and the distribution amplitudes (DAs) for the quarkonia system. For the sake of completeness, we have also included the study of the ground and the first excited states of quarkonia mesons. We have also illustrated the 3D wave functions for the radially excited states in order to study their nodal structures. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, H1(e,e′,π+)n [H. P. Blok (Jefferson Lab Fπ Collaboration), Charged pion form factor between Q2=0.60, and 2.45 GeV2. I. Measurements of the cross section for the H1(e,e′π+)n reaction, .], we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results [H.-M. Choi , Pion off-shell electromagnetic form factors: Data extraction and model analysis, .] from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F1(Q2,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q2,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties. Published by the American Physical Society 2024

Quark counting, Drell-Yan West, and the pion wave function

The relation between the pion's quark distribution function, q(x), its light-front wave function, and the elastic charge form factor, F(Δ2), is explored. The square of the leading-twist pion wave function at a special probe scale, ζH, is determined using models and Poincaré covariance from realistic results for q(x). This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship between q(x) and F(Δ2) is proposed. Published by the American Physical Society 2024

Pion gravitational form factors in the QCD instanton vacuum. I

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024

Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach

We compute the gravitational form factors (GFFs) and study their applications for the description of the mechanical properties such as the pressure, shear force distributions, and the mechanical radius of the proton from its light-front wave functions (LFWFs) based on basis light-front quantization (BLFQ). The LFWFs of the proton are given by the lowest eigenvector of a light-front effective Hamiltonian that incorporates a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling between the constituent quarks solved in the valence Fock sector. We find acceptable agreement between our BLFQ computations and the lattice QCD for the GFFs. Our D-term form factor also agrees well with the extracted data from the deeply virtual Compton scattering experiments at Jefferson Lab, and the results of different phenomenological models. The distributions of pressures and shear forces are similar to those from different models. Published by the American Physical Society 2024

Quark spin-orbit correlations in spin-0 and spin-1 mesons using the light-front quark model

We investigate the spin-orbital angular momentum correlations for the active quark inside the light and heavy mesons for both the spin-0 and spin-1 cases. These correlations can be derived from the generalized transverse-momentum-dependent distributions as well as the generalized parton distributions. We employ the overlap representation of light-front wave functions in the light-front quark model to calculate our analytical results. The dependence of spin-orbit correlations (SOCs) on the longitudinal momentum fraction x as well as the transverse-momentum-dependence k⊥ is graphically presented. Even though the SOCs have already been studied for the spin-0 pions and kaons in other approaches, no calculations for the other light and heavy spin-0 mesons have been reported in the literature. Further, the correlations for any of the light and heavy spin-1 mesons are studied for the first time in the present work. Published by the American Physical Society 2024

Structure of heavy mesons in the light-front quark model

We investigate the structure of ground-state heavy mesons within the light-front quark model, utilizing wave functions derived from the single Gaussian ansatz (SGA) and the Gaussian expansion method (GEM). By performing a χ2 fit to static properties such as mass spectra and decay constants, we determine the model parameters for each approach. We then compare the impacts of both methods on the light-front wave functions and structural observables. Our analysis reveals significant differences in the distribution amplitudes ϕ2;M(x) near the end points, with GEM showing enhanced amplitudes and correct asymptotic behavior ϕ2;M(x→1)∝(1−x), consistent with perturbative QCD. This end point behavior is linked to the short-range (high-momentum) wave function governed by color Coulomb interaction and relativistic kinematics. GEM accurately reproduces a power-law damping ψ0(k→∞)∝1/k⊥2, aligning with perturbative QCD predictions. Furthermore, the electromagnetic form factors of pseudoscalar mesons in the low-Q2 region fall off faster with GEM than with SGA. Overall, while both methods adequately describe static properties, GEM provides a more accurate description of structural properties, being more sensitive to details and asymptotic behaviors. Published by the American Physical Society 2024

Transverse-momentum-dependent gluon distributions of proton within basis light-front quantization

Gluon transverse-momentum dependent distributions (TMDs) are very important for revealing the internal structure of the proton. They correspond to a variety of experiments and are among the major tasks of the future electron-ion colliders. In this paper, we calculate the T-even gluon TMDs at the leading twist within the Basis Light-front Quantization framework. We employ the light-front wave functions of the proton obtained from a light-front quantized Hamiltonian with Quantum Chromodynamics input determined for its valence Fock-sector with three constituent quarks and an additional Fock-sector, encompassing three quarks and a dynamical gluon, with a three-dimensional confinement. After obtaining the numerical results we investigate the properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues inequalities and investigate the correlations between transverse and longitudinal degrees of freedom. With their connection to unintegrated gluon distributions in mind, we further investigate the limiting behaviors of gluon TMDs in the small-x and large-x regions.

Flavor asymmetry of light sea quarks in proton: a light-front spectator model

We formulate a light-front spectator model for the proton that incorporates the presence of light sea quarks. In this particular model, the sea quarks are seen as active partons, whereas the remaining components of the proton are treated as spectators. The proposed model relies on the formulation of the light-front wave function constructed by the soft wall AdS/QCD. The model wave functions are parameterized by fitting the unpolarized parton distribution functions of light sea quarks from the CTEQ18 global analysis. We then employ the light-front wave functions to obtain the sea quarks generalized parton distribution functions, transverse momentum dependent parton distributions, and their asymmetries, which are accessible in the upcoming Electron-Ion-Colliders. We investigate sea quarks’ spin and orbital angular momentum contributions to the proton spin.

Skewed generalized parton distributions of proton from basis light-front quantization

We obtain all the leading-twist quark generalized parton distributions (GPDs) inside the proton at nonzero skewness within the basis light-front quantization framework. We employ the light-front wave functions of the proton from a light-front quantized Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. We find that the qualitative behaviors of our GPDs are similar to those of other theoretical calculations. We further examine the GPDs within the boost-invariant longitudinal coordinate, σ=12b−P+, which is identified as the Fourier conjugate of the skewness. The GPDs in the σ-space show diffraction patterns, which are akin to the diffractive scattering of a wave in optics.

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T++ and T+−, which are used to extract the gravitational form factors A(Q2) and D(Q2). The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

Pseudoscalar Mesons and Emergent Mass

Despite its role in the continuing evolution of the Universe, only a small fraction of the mass of visible material can be attributed to the Higgs boson alone. The overwhelmingly dominant share may/should arise from the strong interactions that act in the heart of nuclear matter; namely, those described by quantum chromodynamics. This contribution describes how studying and explaining the attributes of pseudoscalar mesons can open an insightful window onto understanding the origin of mass in the Standard Model and how these insights inform our knowledge of hadron structure. The survey ranges over distribution amplitudes and functions, electromagnetic and gravitational form factors, light-front wave functions, and generalized parton distributions. Advances made using continuum Schwinger function methods and their relevance for experimental efforts are highlighted.

ρ -meson spectroscopy and diffractive production using the holographic light-front Schrödinger equation and the ’t Hooft equation

We determine the mass spectroscopy and light-front wave functions (LFWFs) of the ρ-meson by solving the holographic Schrödinger equation of light-front chiral QCD along with the ’t Hooft equation of (1+1)-dimensional QCD in the large Nc limit. Subsequently, we utilize the obtained LFWFs in conjunction with the color glass condensate dipole cross section to calculate the cross sections for the diffractive ρ-meson electroproduction. Our spectroscopic results align well with the experimental data. Predictions for the diffractive cross sections demonstrate good consistency with the available experimental data at different energies from H1 and ZEUS collaborations. Additionally, we show that the resulting LFWFs for the ρ-meson can effectively describe various properties, including its decay constant, distribution amplitudes, electromagnetic form factors, charge radius, magnetic and quadrupole moments. Comparative analyses are conducted with experimental measurements and the available theoretical predictions. Published by the American Physical Society 2024

Nonperturbative photon qq¯ light front wave functions from a contact interaction model

We propose a method to calculate the qq¯ light front wave functions (LFWFs) of photons at low virtuality, i.e., the light front amplitude of γ*→qq¯ at low Q2, based on a light front projection approach. We exemplify this method using a contact interaction model within Dyson-Schwinger equations formalism and obtain the nonperturbative photon qq¯ LFWFs. In this case, we find the nonperturbative effects are encoded in the enhanced quark mass and a dressing function of covariant quark-photon vertex, as compared to the leading order quantum electrodynamics photon qq¯ LFWFs. We then use nonperturbative-effect modified photon qq¯ LFWFs to study the inclusive deep inelastic scattering HERA data in the framework of the color dipole model. The results demonstrate that the theoretical description of data at low Q2 can be significantly improved once the nonperturbative corrections are included in the photon LFWFs. Published by the American Physical Society 2024

Leading twist T -even TMDs for the spin-1 heavy vector mesons

We have presented the leading twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 heavy vector mesons J/ψ-meson and ϒ-meson using the overlap of the light-front wave functions. We have computed their TMDs in the light-front holographic model (LFHM) as well as the light-front quark model (LFQM) and further compared the results with the Bethe-Salpeter (BSE) model. We have discussed the behavior of the TMDs with respect to momentum fraction carried by active quark (x) and the transverse quark momenta (k⊥) in both the models. We have also calculated the k⊥ moments of the quark in both the models and have compared the results with the BSE model. The predictions of LFQM are found to be in accord with the BSE model. Further, we have analyzed the leading twist parton distribution functions (PDFs) for both the heavy mesons in both the models and the results are found to be in accord with the basic light-front quantization (BLFQ) and BSE model. Published by the American Physical Society 2024

Exclusive diffractive J/ψ and ψ(2S) production in dipole model using a holographic AdS/QCD light-front wavefunction with longitudinal confinement

We use anti-de Sitter/quantum chromodynamics based holographic light-front wavefunction (LFWF) for vector meson, in conjunction with the dipole model to investigate the cross sections data for the diffractive and exclusive J/ψ and ψ(2S) production. We confront the experimental data using a new explicit form of the holographic LFWF, where the longitudinal confinement dynamics in the light-front Schrödinger equation is captured by the ’t Hooft equation of (1+1)-dim, in large Nc approximation, in addition to the transverse confinement dynamics governed by the confining mass scale parameter κ in vector mesons. We obtain the LFWF parameters from fitting to the exclusive J/ψ electroproduction data from the electron-proton collision at the Hadron Electron Ring Accelerator collider for mc=1.27 GeV. Our results suggest that the dipole model together with holographic meson LFWFs with longitudinal confinement is able to give a successful description for differential scattering cross section for exclusive J/ψ electroproduction for H1 and ZEUS data. We also predict the rapidity distributions of differential scattering cross section and total photoproduction of J/ψ and ψ(2S) states in proton-proton ultraperipheral collisions (UPCs) at center of mass energy s=7,13 TeV. Using the minimum set of parameters, our predictions for the UPCs are in good agreement with the recent experimental observations of UPCs at ALICE and LHCb Collaborations. Published by the American Physical Society 2024

Algebraic model to study the internal structure of pseudoscalar mesons with heavy-light quark content

The internal structure of all lowest-lying pseudoscalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based of the meson’s Bethe-Salpeter amplitude (BSA) and quark’s propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark parton distribution amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudoscalar heavy-light mesons to compute their generalized parton distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related parton distribution functions (PDFs), electromagnetic form factors (EFFs), and impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions. Published by the American Physical Society 2024

Light front approach to axial meson photon transition form factors: Probing the structure of χc1 (3872)

Abstract. We propose to study the structure of the enigmatic χc1(3872) axial vector meson through its γL*γ → χc1 (3872) transition form factor. We use our recently derived light-front wave function representation of the form factor for the lowest cc¯ Fock-state. We found that the reduced width of the state is well within the current experimental bound recently published by the Belle collaboration. This strongly suggests a crucial role of the cc¯ Fock-state in the photon-induced production. Our predictions for the Q2 dependence can be tested by future single tagged e+e− experiments, giving further insights into the short-distance structure of this meson.

Generalized parton distributions of gluon in proton: A light-front quantization approach

We solve for the gluon generalized parton distributions (GPDs) inside the proton at zero skewness, focusing specifically on leading twist chiral-even GPDs. We obtain and employ the light-front wavefunctions (LFWFs) of the proton from a light-front quantized Hamiltonian with Quantum Chromodynamics input using basis light-front quantization (BLFQ). Our investigation incorporates the valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon. We examine the GPDs within impact parameter space and evaluate the x-dependence of the transverse square radius. We find that the transverse size of the gluon at lower-x is larger than that of the quark, while it exhibits opposite behavior at large-x. Using the proton spin sum rule, we also determine the relative contributions of quarks and the gluon to the total angular momentum of the proton.