Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach
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79 ASTRONOMY AND ASTROPHYSICS↗
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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, 1 H(e,e',π + )n, Charged pion form factor between Q 2 = 0.60, and 2.45 GeV 2 . I. Measurements of the cross section for the 1 H(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 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 F 1 (Q 2 ,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(Q 2 ,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.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Light-front wave functions of vector mesons in an algebraic model
Not Available
97 MATHEMATICS AND COMPUTING↗
Instanton Effects in Euclidean vacuum, Real Time Production, and in the Light-front Wave Functions
Nontrivial topological structures of non-Abelian gauge fields were discovered in the 1970s. Instanton solutions, describing vacuum tunneling through topological barriers, have fermionic zero modes which are at the origin of ‘t Hooft effective Lagrangian. In the 1980s, instanton ensembles have been used to explain chiral symmetry breaking. In the 1990s, a large set of numerical simulations were performed deriving Euclidean correlation functions. The special role of scalar diquarks in nucleons and color superconductivity in dense quark matter has been elucidated. In these lectures, we discuss further developments of physics related to gauge topology. We show that the instanton–anti-instanton “streamline” configurations describe “sphaleron transitions” in high-energy collisions, which result in production of hadronic clusters with nontrivial topological/chiral charges. (They are not yet observed, but discussions of dedicated experiments at the LHC and RHIC are ongoing.) Another new direction is instanton effects in hadronic spectroscopy, both in the rest frame and on the light front. We will discuss their role in central and spin-dependent potentials, form factors and antiquark nuclear “sea”. Finally, we summarize the advances in the semiclassical theory of deconfinement, and chiral phase transitions at finite temperature, in QCD, and in some of its “deformed” versions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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(Δ 2 ), is explored. The square of the leading-twist pion wave function at a special probe scale, 𝜁 𝐻 , 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(Δ 2 ) is proposed.
Form factors↗
Transverse structure of the pion beyond leading twist with basis light-front quantization
We investigate the twist-3transverse-momentum-dependent parton distribution functions (TMDs) of the pion with basis light-front quantization. The twist-3 TMDs are not independent and can be decomposed into twist-2and genuine twist-3 terms from the equations of motion (EOM). We compute the TMDs from the resulting light-front wave functions obtained by diagonalizing the light-front QCD Hamiltonian, determined for pion’s constituent quark-antiquark and quark-antiquark-gluon Fock sectors, with three-dimensional confinement. We also obtain the twist-3 parton distribution functions (PDFs) and show that they preserve the sum rule, which affirms the robustness of our approach. This is the first time that theoretical predictions are made for subleading twist structures of the pion containing interference terms between two light-front Fock sectors.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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
Astronomy & Astrophysics↗
Basis light-front quantization for the Λ b and Σ b baryons
Within the basis light-front quantization framework, we compute the masses and light-front wave functions of the Λ b baryon and its isospin triplet counterparts Σ b + , Σ b 0 , and Σ b − using a light-front effective Hamiltonian in the leading Fock sector. These wave functions are obtained as eigenstates of the effective Hamiltonian, which incorporates the one-gluon exchange interaction with fixed coupling and a three-dimensional confinement potential. With the quark masses and the couplings as adjustable parameters, the computed masses are set within the experimental range. The resulting predictions for their electromagnetic properties align well with other theoretical calculations. Additionally, the parton distribution functions (PDFs) of these baryons are obtained for the first time, with gluon and sea quark distributions dynamically generated through QCD evolution of the valence quark PDFs. Published by the American Physical Society 2025
Meng, Lingdi (ORCID:0009000096439904)↗
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 ( Q 2 ) and D ( Q 2 ) . 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
Astronomy & Astrophysics↗
Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging
We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (previous article), we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant three-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum (𝐷/𝑆 wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta of approximately 300 MeV, which select configurations with a large 𝐷 wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Twist-3 generalized parton distribution for the proton from basis light-front quantization
We investigate the twist-3 generalized parton distributions (GPDs) for the valence quarks of the proton within the basis light-front quantization (BLFQ) framework. We first solve for the mass spectra and light-front waved functions (LFWFs) in the leading Fock sector using an effective Hamiltonian. Using the LFWFs we then calculate the twist-3 GPDs via the overlap representation. By taking the forward limit, we also get the twist-3 parton distribution functions (PDFs), and discuss their properties. Our prediction for the twist-3 scalar PDF agrees well with the CLAS experimental extractions.
Astronomy & Astrophysics↗
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 Q 2 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
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Color Transparency and Light-Front Holographic QCD
Color transparency, the reduction of initial-state or final-state interactions in coherent nuclear processes, is a natural prediction of QCD (quantum chromodynamics) provided that small-sized or point-like configurations (PLCs) are formed in high-momentum transfer, high-energy, semi-exclusive processes. I use the Frankfurt-Miller-Strikman criteria for the existence of PLCs to show that the wave functions of light-front holographic QCD, as currently formulated, do not contain a PLC.
Miller, Gerald A. (ORCID:0000000324433639)↗
Stronger C -odd color charge correlations in the proton at higher energy
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Residual mean field model of valence quarks in the nucleon
Abstract We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark–quark interactions that generate the high x tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $$x_p$$ x p , of the peak of $$xq_V(x)$$ x q V ( x ) distribution of the valence quark and the effective mass of the residual system, $$m_R$$ m R , in the form: $$x_{p} \approx {1\over 4} (1-{m_R\over m_N})$$ x p ≈ 1 4 ( 1 - m R m N ) at starting $$Q^2$$ Q 2 . This relation explains the difference in the peak positions for d- and u-quarks through the expected difference of residual masses for valence d- and u-quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u-quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mixing effects on spectroscopy and partonic observables of heavy mesons with logarithmic confining potential in a light-front quark model
Using the variational principle, we systematically investigate the mass spectra and wave functions of both 1𝑆 and 2𝑆 state heavy pseudoscalar (𝑃) and vector (𝑉) mesons within the light-front quark model. This approach incorporates a Coulomb plus logarithmic confinement potential to accurately describe the constituent quark and antiquark dynamics. Additionally, spin hyperfine interactions are introduced perturbatively to compute the masses of pseudoscalar and vector mesons. The present analyses of the 1𝑆 and 2𝑆 states require the consideration of mixing between them to account for empirical constraints. These constraints include the mass gap Δ𝑀 𝑃 >Δ𝑀 𝑉 , where Δ𝑀 𝑃(𝑉) =𝑀$^{2𝑆}_{𝑃(𝑉)}$−𝑀$^{1𝑆}_{𝑃(𝑉)}$ and the hierarchy of the decay constants 𝑓 1𝑆 >𝑓 2𝑆 . We find the optimal value of the mixing angle to be 𝜃 =18°, significantly enhancing the consistency between our spectroscopic predictions and the experimental data compiled by the Particle Data Group. Furthermore, based on the predicted mass, the newly observed resonance 𝐵 𝐽 (5840) could be assigned as a 2 1 𝑆 0 state in the 𝐵 meson family. The study also reports various pertinent observables, including twist-two distribution amplitudes, electromagnetic form factors, charge radii, 𝜉 moments, and transition form factors that are found to be consistent with both available lattice simulations and experimental data. In addition, our predicted branching ratios for the channels of 𝐵 + →𝜏 + 𝜈 𝜏 as well as rare decays of 𝐵 0 and 𝐵$^0_𝑠$ appear in accordance with experimental data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Observables for scattering on targets with arbitrary spin
Starting from the Weinberg formalism for fields of arbitrary spin, we discuss a method for the decomposition of matrix elements of QCD operators (local currents, quark/gluon bilinears) for targets with arbitrary spin. This procedure is advantageous for the systematic study of the structure of hadrons and nuclei, particularly in the case of spin-dependent observables. As higher spin targets exhibit new features in their hadronic structure, the investigation of these properties can enhance our understanding of the strong force. The construction allows for a unified framework to discuss spin > 1/2 very similar to the spin 1/2 case, without subsidiary conditions for the wave functions. Different types of spinors (canonical, helicity, light-front helicity) can be easily accommodated. Its numerical implementation is simple and can be entirely reduced to objects familiar from the rotation group. A natural sl(2,C) multipole decomposition emerges, enabling a physical interpretation of non-perturbative objects that multiply spinor bilinears as Generalized Form Factors. To demonstrate the efficacy of this method, we apply it to the description of a spin 1 target, such as the deuteron. We discuss extensions of the formalism to hard exclusive processes on the deuteron and beyond.
Vera, Frank↗
Superfast quarks in deuterium
An extension to our previous study on nuclear parton distribution functions (nPDFs) [Kim and Miller, Phys. Rev. C 106, 055202 (2022)] using light-front holographic quantum chromodynamics (LFHQCD) [Brodsky, de Teramond, Dosch, and Erlich, Phys. Rep. 584, 1 (2015)] is presented. We apply the effects of nucleon motion inside the nucleus (Fermi motion/smearing) to deuterium, extending our deuterium nPDFs to the superfast , 𝑥 > 1, region [Frankfurt and Strikman, Phys. Rep. 160, 235 (1988)] where we estimate our results to be reasonable up to 𝑥 ≈ 1.7. We utilize four different deuteron wave functions (AV18, NijmI, NijmII, Nijm93). We find that our model, with no additional new parameters, shows very good agreement with deuterium EMC ratio data obtained from the BONuS experiment [Fenker et al., Nucl. Instrum. Methods Phys. Res. A 592, 273 (2008); Baillie et al. (CLAS Collaboration), Phys. Rev. Lett. 108, 142001 (2012); Phys. Rev. Lett. 108, 199902(E) (2012); Tkachenko et al. (CLAS Collaboration), Phys. Rev. C 89, 045206 (2014); Phys. Rev. C 90, 059901(E) (2014); Griffioen et al., Phys. Rev. C 92, 015211 (2015)]. Looking beyond conventional nuclear physics, and in anticipation of 12 GeV experiments at Jefferson Lab, we use a LFHQCD ansatz to predict the contributions of an exotic six-quark state to the deuteron 𝐹 2 structure function, 𝐹$^D_2$, in the superfast region. We find that the effects of using other potentials are about the same magnitude as six-quark effects—both have small effects in 𝑥 < 1, but have significant contributions at 𝑥 > 1.
Physics↗