Light-front Wave Functions Research Articles

Two-body light front wave functions from general AdS/QCD models

In this work, we consider an extension to the matching procedure proposed by Brodsky and de Teramond to obtain the two-body wave functions in the light-front formalism for holographic models. We compute the light-front wave function (LFWF) considering different static dilaton fields and AdS-like geometric deformations. We also prove that this procedure holds for general AdS/QCD models in asymptotically AdS geometries.

Frame-independent spatial coordinate z̃ : Implications for light-front wave functions, deep inelastic scattering, light-front holography, and lattice QCD calculations

A general procedure for obtaining frame-independent three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$ is the boost and Lorentz frame-independent coordinate conjugate to the light-front momentum coordinate $x=\frac{{k}^{+}}{{P}^{+}}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution function of hadrons as an integral over the frame-independent longitudinal distance (the Ioffe time) between virtual-photon absorption and emission appearing in the forward virtual photon-hadron Compton scattering amplitude. Specific examples using models derived from light-front holographic QCD show that the spatial extent of the proton eigenfunction in the longitudinal direction can have a very large extent in $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$.

Parton distribution functions of heavy mesons on the light front

The parton distribution functions (PDFs) of heavy mesons are evaluated from their light-front wave functions, which are obtained from a basis light-front quantization in the leading Fock sector representation. We consider the mass eigenstates from an effective Hamiltonian consisting of the confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with running coupling. We present the gluon and the sea quark PDFs which we generate dynamically from the QCD evolution of the valence quark distributions.

Pion-nucleus induced Drell-Yan cross section in models inspired by light-front holography

We evaluate the cross section for the pion induced Drell-Yan process in two different models of the pion light-front wave function, inspired by light-front holographic approaches. We obtain the valence quark distribution functions in those models, which after QCD evolution, are consistent with the experimental data from the E-0615 experiment at Fermilab. Supplemented by the parton distribution functions of the target nuclei, we obtain the cross section consistent with the experimental data for the π− Nucleus →μ+μ−X Drell-Yan process.

Sivers and Boer–Mulders GTMDs in light-front holographic quark–diquark model

We calculate the time reversal odd (T-odd) generalized transverse momentum dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We have incorporated both scalar and axial vector diquarks in the model and obtained an overlap representation of the GTMDs using the light-front wave functions (LFWFs). Contribution from the final state interaction is incorporated at the level of one gluon exchange as a phase factor in the LFWF. We show that the final state interaction term can be factored out in this model and this part is the same for both GTMDs. We also present the corresponding Wigner distributions.

Heavy-light mesons on the light front

We study the heavy-light mesons within basis light-front quantization. The resulting mass spectra of D, D_s, B, and B_s agree reasonably well with experiments. We also predict states which could be measured in the near future. In the light-front formalism, we calculate the light-front wave functions and additional experimental observables, such as parton distribution functions, distribution amplitudes, and decay constants by means of integrations over light-front wave functions. We also provide ratios of decay constants for selected pseudoscalar meson decays (D_s to D and B_s to B) as they may prove to be theoretically more robust and more reliably determined in experiments. We find that our ratios are systematically smaller than existing experiments and other approaches by 5–18%.

Spatial and momentum imaging of the pion and kaon

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multi-dimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: $\langle \vec{b}_T^2\rangle_{u}^\pi=0.11$fm$^2$, $\langle \vec{b}_T^2\rangle_{s}^K=0.08$fm$^2$, and $\langle \vec{b}_T^2\rangle_{u}^K=0.13$fm$^2$, and therefore the $s$ quark in the kaon is much closer to the center of transverse momentum than the $u$ quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60\% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full DSE calculation (containing an infinite tower of Fock states) for the pion form factor.

Basis light-front quantization for a chiral nucleon-pion Lagrangian

We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.

Pion and kaon parton distribution functions from basis light front quantization and QCD evolution

We investigate the parton distribution functions (PDFs) of the pion and the kaon by combining quantum chromodynamics (QCD) evolution with the basis light front quantization. The initial PDFs result from the light front wave functions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu--Jona-Lasinio interactions. The valence-quark PDF of the pion, after QCD evolution, is consistent with the result from the E-0615 experiment at Fermilab. Meanwhile, the pion structure function calculated from the PDFs agrees with the ZEUS and the H1 experiments at DESY-HERA for large $x$. Additionally, the ratio of the up quark PDF of the kaon to that of the pion is in agreement with the NA-003 experiment at CERN. We also present the cross section for the pion-nucleus induced Drell-Yan process with the obtained pion PDFs supplemented by the PDFs of the target nuclei.

Study of Spin–Spin Correlations between Quark and a Spin-1/2 Composite System

We study the correlation between the fermion composite system and quark spins by using the light-cone quark–diquark model. We do the calculations for u-quark and d-quark in the fermion system by considering different polarization configurations of both. The contribution from scalar and axial-vector diquarks is taken into account. The overlap representation of light-front wavefunctions is used for the calculations. The spin–spin correlations for u and d quarks are presented in transverse impact-parameter plane and transverse momentum plane as well.

Light-front wave functions of mesons, baryons, and pentaquarks with topology-induced local four-quark interaction

We calculate light-front wave functions of mesons, baryons and pentaquarks in a model including constituent mass (representing chiral symmetry breaking), harmonic confining potential, and 4-quark local interaction of 't Hooft type. The model is a simplified version of that used by Jia and Vary. The method used is numerical diagonalization of the Hamiltonian matrix, with certain functional basis. We found that the nucleon wave function displays strong diquar correlations, unlike that for Delta (decuplet) baryon. We also calculate 3-quark-5-quark admixture to baryons, and the resulting antiquark sea PDF.

Double parton distributions for a positroniumlike bound state using light-front wave functions

We investigate the double parton distributions (DPDs) for a positronium-like bound state using light-front QED. We incorporate the higher Fock three particle component of the state, that includes a photon. We obtain the overlap representation of the DPDs in terms of the three-particle light-front wave functions (LFWFs). Our calculation explores the correlations between the momentum fractions of the particles probed and the transverse distance between them, without any assumption of factorization between them. We also investigate the behavior of the DPDs near the kinematical boundary when the sum of the momentum fractions is close to one.

γ*γ*→ηc(1S,2S) transition form factors for spacelike photons

We derive the light-front wave function (LFWF) representation of the $\gamma^* \gamma^* \to \eta_c(1S)\,,\eta_c(2S)$ transition form factor $F(Q_1^2, Q_2^2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schr\"odinger equation for a variety of $c \bar c$ potentials. We compare our results to the BaBar experimental data for the $\eta_c(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. We present some examples of two-dimensional distributions for $F (Q_1^2,Q_2^2)$. A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be almost model independent. Factorization is shown to be strongly broken, and a scaling of the form factor as a function of $\bar Q^2 = (Q_1^2 + Q_2^2)/2$ is obtained.

Heavy quarkonia production at energies available at the CERN Large Hadron Collider and future electron-ion colliding facilities using basis light-front quantization wave functions

We study exclusive charmonium and bottomonium production in ultra-peripheral heavy-ion collisions and electron-ion collisions within the dipole picture. We employ heavy quarkonium light-front wavefunctions obtained within the basis light-front quantization framework, which has some features of the light-front holographic QCD. We focus on comparison with measurements of exclusive charmonium and bottomonium production in ultraperipheral $pp$, $p$Pb and PbPb collisions at LHC and find reasonable agreement with the cross sections. We also discuss the coherent production cross-section ratios of excited states to the ground state for charmonium and bottomonium, which exhibit insensitivity to the dipole model parameters. We show that electron-ion collisions provide an opportunity for a quantitative study of heavy quarkonium structure.

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.

A complete set of in-medium splitting functions to any order in opacity

In this Letter we report the first calculation of all O(αs) medium-induced branching processes to any order in opacity. Our splitting functions results are presented as iterative solutions to matrix equations with initial conditions set by the leading order branchings in the vacuum. The flavor and quark mass dependence of the in-medium q→qg, g→gg, q→gq, g→qq¯ processes is fully captured by the light-front wavefunction formalism and the color representation of the parent and daughter partons. We include the explicit solutions to second order in opacity as supplementary material and present numerical results in a realistic strongly-interacting medium produced in high center-of-mass energy heavy ion collisions at the Large Hadron Collider. Our numerical simulations show that the second order in opacity corrections can change the energy dependence of the in-medium shower intensity. We further find corrections to the longitudinal and angular distributions of the in-medium splitting kernels that may have important implications for jet substructure phenomenology.

Using QCD counting rules to identify the production of gluonium

The empirical identification of bound states of gluons has remained a central goal of hadron spectroscopy. We suggest an experimentally challenging, but model–independent way to assess which zero charge, isospin-zero mesons have a large gluonium light-front wavefunction component in the quark and gluon Fock space of QCD. Our method exploits QCD counting rules which relate the power-law fall-off of production amplitudes at high momentum transfer to the meson's twist (dimension minus spin of its minimum interpolating operators). Scalar 0+ glueballs composed of two valence gluons with zero internal orbital angular momentum have twist τ=2. In contrast, quark-antiquark |qq¯〉 scalar mesons have twist τ≥3 since they have nonzero orbital angular momentum, and multi-quark states such as |qqq¯q¯〉 tetraquarks yield twist τ≥4. Thus, the production cross section for both |qq¯〉 and |qqq¯q¯〉 mesons will be suppressed by at least one power of momentum transfer relative to glueball production. For example, in single inclusive particle hadroproduction AB→CX, the cross section for glueball production at high transverse momentum pT and fixed xT=2pTs will dominate higher twist mesons by at least two powers of pT.Similarly, in exclusive production processes at large CM energy and fixed CM angle, the glueball rate dominates by a power of s: we illustrate the method with a simple reaction, e−e+→ϕf0 where the f0 can be tested to be a glueball versus another type of scalar meson.

Form factors and generalized parton distributions of heavy quarkonia in basis light front quantization

We calculate the electromagnetic (charge, magnetic and quadrupole) form factors and the associated static moments of heavy quarkonia (charmonia and bottomonia) using the Basis Light Front Quantization (BLFQ) approach. For this work, we adopt light front wavefunctions (LFWFs) generated by a holographic QCD confining potential and a one-gluon exchange interaction with fixed coupling. We compare our BLFQ results with the limiting case of a single BLFQ basis state description of heavy quarkonia and with other available results. These comparisons provide insights into relativistic effects. Using the same LFWFs generated in the BLFQ approach, we also present the generalized parton distributions (GPDs) for selected mesons including those for radially excited mesons such as $\psi^\prime$ and $\Upsilon^\prime$. Our GPD results establish the foundation within BLFQ for further investigating hadronic structure such as probing the spin structure of spin-one hadrons in the off-forward limit.

Basis light front quantization for the charged light mesons with color singlet Nambu–Jona-Lasinio interactions

We apply the basis light front quantization (BLFQ) approach to describe the valence structures of the charged light meson ground states. Specifically, the light front wavefunctions of $\pi^\pm$, $\rho^\pm$, $K^\pm$, and $K^{*\pm}$ are obtained as the eigenvectors of the light front effective Hamiltonians with confinement potentials supplemented by the color singlet Nambu--Jona-Lasinio (NJL) interactions. We adjust our model such that the spectrum of these ground states and the charge radii of the pseudoscalar states agree with experimental results. We present the elastic form factors and parton distribution amplitudes (PDAs) as illustrations of the internal structures of the pseudoscalar pions and kaons in terms of valence quarks.

Intrinsic Transverse Motion of the Pion's Valence Quarks.

Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's l_{z}=0 and |l_{z}|=1 leading Fock-state light-front wave functions (LFWFs) [labeled by ψ_{l_{z}}(x,k_{T}^{2})]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction x. The LFWFs have a nontrivial (x,k_{T}^{2}) dependence and in general do not factorize into separate functions of each variable. For k_{T}^{2}≲1 GeV^{2} the k_{T}^{2} dependence of the LFWFs is well described by a Gaussian; however for k_{T}^{2}≳10 GeV^{2} these LFWFs behave as ψ_{0}∝x(1-x)/k_{T}^{2} and ψ_{1}∝x(1-x)/k_{T}^{4}, and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. The TMD evolution of our result is studied using both the b^{*} and ζ prescriptions which allows a qualitative comparison with Drell-Yan data.