Light-front Wave Functions Research Articles

Nucleon structure from a light-front hamiltonian


 
 
 We obtain the light-front wave functions (LFWFs) of the nucleon in the leading Fock sector representation using basis light-front quantization (BLFQ) approach. We adopt a light-front effective Hamiltonian, which includes a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling, and solve for it mass eigenstates. We then employ the LFWFs to compute the axial form factor and the transverse charge and magnetization densities for the nucleon. The axial form factor is found to be consistent with the experimental data. The charge and magnetization densities agree qualitatively with the phenomenological fits.
 
 

Transverse momentum distributions of valence quarks in light and heavy vector mesons

We study the leading-twist time-reversal even transverse momentum-dependent parton distribution functions (TMDs) of light and heavy vector mesons, i.e., the $\ensuremath{\rho}$, $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}$. We employ the leading Fock-state light front wave functions (LF-LFWFs) of $\ensuremath{\rho}$ and $J/\ensuremath{\psi}$ from our recent study, and supplement with $\mathrm{\ensuremath{\Upsilon}}$'s LF-LFWFs. These LF-LFWFs are extracted from dynamically solved Bethe-Salpeter wave functions. The vector meson TMDs are then studied with the light front overlap representation at leading Fock-state. All the obtained TMDs are nonvanishing and evolve with current quark mass, in particular the tensor polarized TMDs ${f}_{1LT}$ and ${f}_{1TT}$ which undergo a sign flip. The $\ensuremath{\rho}$ TMDs are compared with other model studies and agreement is found, aside from ${f}_{1LT}$ and ${f}_{1TT}$. Finally, the collinear PDFs of vector mesons are studied. The $\ensuremath{\rho}$'s valence PDFs ${f}_{1,v}(x)$ and ${g}_{1L,v}(x)$ are evolved to the scale of 2.4 GeV, with their first three moments compared to the lattice QCD prediction. The qualitative behavior of tensor polarized PDF ${f}_{1LL}(x)$ in $\ensuremath{\rho}$ at large $x$ is also discussed.

Pion inspired by QCD: Nakanishi and light-front integral representations

The pion structure in Minkowski space is explored using the Nakanishi integral representation. A general framework is developed for the pion Bethe-Salpeter amplitude based on the K\"allen-Lehmann representation of the dressed quarks with an ansatz for the pseudoscalar $\ensuremath{\pi}\ensuremath{-}q\overline{q}$ vertex fulfilling the axial Ward-Takahashi identity. The Nakanishi weight functions are derived for the scalar amplitudes associated with the decomposition of the pion Bethe-Salpeter amplitude in different operator bases in the Dirac spinor space in terms of the involved spectral densities. The approach is applied to an analytical model of the pion Bethe-Salpeter amplitude, which is combined with Landau gauge lattice QCD results for the quark running mass at spacelike momentum. From the Nakanishi integral representation several pion observables were calculated, such as the decay constant, the spin decomposition of the valence probabilities, longitudinal and transverse momentum distributions from the valence component of the light-front wave function.

Prompt hadroproduction of C-even quarkonia in the light-front $k_T$ -factorization approach

We present a new approach for the prompt production of quarkonia which is based on the k_TkT-factorization method. The production of even C-parity quarkonia proceeds via the fusion of two (off-shell) gluons. Especially in the kinematics of the LHCb experiment these processes are thus expected to be a sensitive probe of the small-xx gluon distribution. We calculate the relevant off-shell matrix elements in terms of the light-front wave functions of the quarkonium states. We present our results for scalar and pseudoscalar charmonia and discuss photon transition form factors as well as cross sections for prompt hadroproduction. We compare our results for the \eta_cηc to recent LHCb data.

Predictions for the Sivers single-spin asymmetry from holographic QCD

A new approach to nonperturbative QCD, holographic light-front QCD, provides a comprehensive model for hadron dynamics and spectroscopy, incorporating color confinement, a universal hadron mass scale, the prediction of a massless pion in the chiral limit, and connections between the spectroscopy of mesons, baryons and tetraquarks across the full hadron spectrum. In this article we present predictions for the Sivers asymmetry and related transverse momentum distributions for the proton based on the light-front wavefunctions of the baryon eigenstate predicted by holographic QCD.

Pion model with the Nakanishi integral representation

In the present work, we describe a model for the pion based on an analytic expression for the Bethe-Salpeter (BSA) amplitude, combined with some ingredients from Lattice QCD calculations. The running quark mass function M(p2), used here, reproduces well the results of Lattice QCD calculations. The analytical form of the running quark mass function contains a single time-like pole, which implies in time-like poles of the dressed quark propagator. Such a form allows to build the weight functions, Gi(γ, z), for the Nakanishi integral representation of each scalar function, χi(k, p), appearing in the decomposition of the Bethe-Salpeter amplitude in terms of Dirac operators. Such scalar amplitudes can also be used to obtain the pion valence light-front wave function.

Highlights of pion and kaon structure from continuum analyses

One of the biggest challenges in contemporary physics is understanding the origin and dynamics of the internal structure of hadrons which, at a fundamental level, is described by quantum chromodynamics (QCD). Taking great prominence amongst hadrons are pions and kaons which, despite being the lightest hadrons in nature, their very existence is intimately connected to those mechanisms responsible for almost all of the mass of the visible matter. In this manuscript we discuss many aspects of the pion and kaon structure via light front wave functions and generalized parton distributions, and a collection of other distributions and structural properties that are inferred therefrom.

Internal structure of pion and kaon: an algebraic model and its implications

We describe an algebraic approach to address aspects of the structure of pseudo-scalar mesons through their corresponding generalized parton distributions, from which parton distribution functions and electromagnetic form factors can be derived. A direct relation between such distributions and the so-called parton distribution amplitudes can be established since the generalized parton distributions are obtained from the overlap of light-front wave functions.

Quark and gluon entanglement in the proton on the light cone at intermediate x

In QCD with ${N}_{c}$ colors the antisymmetric valence quark color space singlet state $\ensuremath{\sim}{\ensuremath{\epsilon}}_{{i}_{1}\ensuremath{\cdots}{i}_{{N}_{c}}}|{i}_{1},\dots{},{i}_{{N}_{c}}⟩$ of the proton corresponds to the reduced density matrix ${\ensuremath{\rho}}_{ij}=(1/{N}_{c}){\ensuremath{\delta}}_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, ${\ensuremath{\lambda}}_{i}=1/{N}_{c}$, the purity $\mathrm{tr}{\ensuremath{\rho}}^{2}=1/{N}_{c}$, and the von Neumann entropy ${S}_{\mathrm{vN}}=\mathrm{log}({N}_{c})$ all indicate maximal entanglement of color. On the other hand, for ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field [E. Witten, Nucl. Phys. B160, 57 (1979)] where there is no entanglement of spatial degrees of freedom. A model calculation at ${N}_{c}=3$ using a simple three quark model light front wave function by Brodsky and Schlumpf predicts percent level entanglement of spatial degrees of freedom. Using light cone perturbation theory, we also derive the density matrix associated with the four parton $|qqqg⟩$ Fock state. Tracing out the quarks, we construct the reduced density matrix for the degrees of freedom of the gluon, which encodes its entanglement with the sources. Our expressions provide the dependence of the density matrix on the soft cutoff $x$ for the gluon light cone momentum, and on the collinear and ultraviolet regulators. Numerical results obtained in a simple approximation indicate stronger entanglement for the gluon (with ${x}_{g}<⟨{x}_{q}⟩$) than for quarks in the three quark Fock state.

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

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.

Residual mean field model of valence quarks in the nucleon

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, of the peak of xq_V(x) distribution of the valence quark and the effective mass of the residual system, m_R, in the form: x_{p} approx {1over 4} (1-{m_Rover m_N}) at starting 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.

Basis light-front quantization approach to photon

We solve for the light-front wave functions (LFWFs) of the physical photon from the eigenvectors of the light-front quantum electrodynamics (QED) Hamiltonian with the aim to determine its bare photon and electron-positron Fock components. We then employ the resulting LFWFs to compute the transverse momentum dependent parton distributions (TMDs) and the generalized parton distributions (GPDs) at zero skewness of the photon. The TMDs are found to be in excellent agreement with the lowest-order perturbative results calculated using the electron-positron quantum fluctuation of the photon. The GPDs are also consistent with the perturbative calculations.

Instanton Effects in Euclidean vacuum, Real Time Production, and in the Light-front Wave Functions

Instanton Effects in Euclidean vacuum, Real Time Production, and in the Light-front Wave Functions

Instanton-induced effects in interquark forces, light-front wave functions and formfactors

Exclusive processes are traditionally described by perturbative hard blocks and “distribution amplitudes" (DAs), matrix elements of operators of various chiral structure and twist. One paper (with I.Zahed) calculate instanton contribution to hard blocks, which is found comparable to perturbative one in few-GeV2 Q2 region of interest. Another paper aims at comprehensive wave functions of mesons, baryons and pentaquarks. The last ones are also included as 5-quark component of the baryons. The calculation, using ’t Hooft operator, gives x-dependence and magnitude of the antiquark PDF. It explains long standing issue of strong flavor asymmetry of antiquark sea. The third paper (also with I.Zahed) is semi-review on the instanton-sphaleron processes in QCD and electroweak theories, with emphasis on their possible experimental observation via double diffractive events at LHC and RHIC. Insert your english abstract here.

Ab initio coupling of jets to collective flow in the opacity expansion approach

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of the moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to collective flow of the quark-gluon plasma in heavy-ion collisions and to the orbital motion of partons in cold nuclear matter in deep inelastic scattering at the electron-ion collider. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that these effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant sub-eikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q \rightarrow q g$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter.

Nucleon structure from basis light-front quantization

We produce the light-front wave functions (LFWFs) of the nucleon from a basis light-front approach in the leading Fock-sector representation. We solve for the mass eigenstates from a light-front effective Hamiltonian, which includes a confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with fixed coupling. We then employ the LFWFs to obtain the electromagnetic and axial form factors, the parton distribution functions (PDFs), and the generalized parton distribution functions for the nucleon. The electromagnetic and axial form factors of the proton agree with the experimental data, whereas the neutron form factors deviate somewhat from the experiments in the low-momentum transfer region. The unpolarized, the helicity, and the transversity valence quark PDFs, after QCD scale evolution, are fairly consistent with the global fits to the data at the relevant experimental scales. The helicity asymmetry for the down quark also agrees well with the measurements; however, the asymmetry for the up quark shows a deviation from the data, especially in the small $x$ region. We also find that the tensor charge agrees well with the extracted data and the lattice QCD predictions, while the axial charge is somewhat outside the experimental error bar. The electromagnetic radii of the protons, the magnetic radius of the neutron, and the axial radius are in excellent agreement with the measurements, while the neutron charge radius deviates from the experiment.

Pion to photon transition form factors with basis light-front quantization

We obtain the distribution amplitude (DA) of the pion from its light-front wave functions in the basis light-front quantization framework. This light-front wave function of the pion is given by the lowest eigenvector of a light-front effective Hamiltonian consisting a three-dimensional confinement potential and the color-singlet Nambu--Jona-Lasinion interaction both between the constituent quark and antiquark. The quantum chromodynamics (QCD) evolution of the DA is subsequently given by the perturbative Efremov-Radyushkin-Brodsky-Lepage evolution equation. Based on this DA, we then evaluate the singly and doubly virtual transition form factors in the space-like region for $\pi^0\rightarrow \gamma^*\gamma$ and $\pi^0\rightarrow \gamma^*\gamma^*$ processes using the hard-scattering formalism. Our prediction for the pion-photon transition form factor agrees well with data reported by the Belle Collaboration. However, in the large $Q^2$ region it deviates from the rapid growth reported by the BaBar Collaboration. Meanwhile, our result on the $\pi^0\rightarrow \gamma^*\gamma^*$ transition form factor is also consistent with other theoretical approaches and agrees with the scaling behavior predicted by perturbative QCD.

Ground state pseudoscalar mesons on the light front: From the light to heavy sector

We extract the leading Fock-state light front wave functions (LF-LFWFs) of both the light and heavy pseudoscalar mesons, e.g., the pion (at masses of 130 MeV, 310 MeV and 690 MeV), $\eta_c$ and $\eta_b$, from their covariant Bethe-Salpeter wave functions within the rainbow-ladder (RL) truncation. It is shown that the LF-LFWFs get narrower in $x$ (the longitudinal momentum fraction of meson carried by the quark) with the increasing current quark mass, and the leading twist parton distribution amplitudes (PDAs) inherit this feature. Meanwhile, we find in the pion the LF-LFWFs only contribute around 30\% to the total Fock-state normalization, indicating the presence of significant higher Fock-states within. In contrast, in the $\eta_c$ and $\eta_b$ the LF-LFWFs contribute more than $90$\%, suggesting the $Q\bar{Q}$ valence Fock-state truncation as a good approximation for heavy mesons. We thus study the 3-dimensional parton distributions of the $\eta_c$ and $\eta_b$ with the unpolarized generalized parton distribution function (GPD) and the transverse momentum dependent parton distribution function (TMD). Through the gravitational form factors in connection with the GPD, the mass radii of the $\eta_c$ and $\eta_b$ in the light-cone frame are determined to be $r_{E,{\rm LC}}^{\eta_c} =0.150$ fm and $r_{E,{\rm LC}}^{\eta_b} =0.089$ fm respectively.

Light front wave functions and diffractive electroproduction of vector mesons

We determine the leading Fock-state light front wave functions (LF-LFWFs) of the $\rho$ and J/$\psi$ mesons, for the first time from the Dyson-Schwinger and Bethe-Salpeter equations (DS-BSEs) approach. A unique advantage of this method is that it renders a direct extraction of LF-LFWFs in presence of a number of higher Fock-states. Modulated by the current quark mass and driven by the dynamical chiral symmetry breaking (DCSB), we find the $\rho$ and $J/\psi$ LF-LFWFs different in profile, i.e., the former are broadly distributed in $x$ (the longitudinal light-cone momentum fraction of meson carried by quark) while the latter are narrow. Moreover, the $\rho$ LF-LFWFs contribute less than 50% to the total Fock-state normalization, suggesting considerable higher Fock-states in $\rho$. We then use these LF-LFWFs to study the diffractive $\rho$ and $J/\psi$ electroproduction within the dipole picture. The calculated cross section shows general agreement with HEAR data, except for growing discrepancy in $\rho$ production at low photon virtuality. Our work provides a first dipole picture analysis on diffractive $\rho$ electroproduction that confronts the parton nature of the light (anti)quarks.