We study the structure of the $ρ$-meson within a light-front model with constituent quark degrees of freedom. We calculate electroweak static observables: magnetic and quadrupole moments, decay constant and charge radius. The prescription used to compute the electroweak quantities is free of zero modes, which makes the calculation implicitly covariant. We compare the results of our model with other ones found in the literature. Our model parameters give a decay constant close to the experimental one.
We summarize the light-front coupled-cluster (LFCC) method for the solution of field-theoretic bound-state eigenvalue problems and indicate the connection with light-front holographic QCD. This includes a sample application of the LFCC method and leads to a relativistic quark model for mesons that adds longitudinal dynamics to the usual transverse light-front holographic Schrodinger equation.
Light-Front Quantization -- Dirac's "Front Form" -- provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic LFWFs. One obtains new insights into the hadronic mass scale, the hadronic spectrum, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons. I also discuss evidence …
Light-front QCD is studied by the method of flow equations. Dynamical gluon mass is generated, which evolves with the cut-off according to renormalization group equation. Eliminating by flow equations the quark gluon coupling with the dynamical gluon mode, one obtains an effective interaction between quark and antiquark which exibits the Coulomb and confining singularities. The scale, which regulates the light-front IR singularities in the gluon sector, defines the string tension of confining interaction. The mechanism of confinement in the light-front formalism is suggested, based on the sing…
Light-front holography allows hadronic amplitudes in the AdS/QCD fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The AdS coordinate z is identified with an invariant light-front coordinate zeta which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wav…
We elaborate the frame dependence of the angular conditions for spin-1 form factors. An extra angular condition is found in addition to the usual angular condition relating the four helicity amplitudes. Investigating the frame-dependence of the angular conditions, we find that the extra angular condition is in general as complicated as the usual one, although it becomes very simple in the $q^+ = 0$ frame involving only two helicity amplitudes. It is confirmed that the angular conditions are identical in frames that are connected by kinematical transformations. The high $Q^2$ behaviors of the p…
In the first part of my lectures, I will use the example of deep-inelastic scattering to explain why light-front coordinates play a distinguished role in many high energy scattering experiments. After a brief introduction into the concept of light-front quantization, I will show that the vacuum for any light-front Hamiltonian is trivial, i.e. the same as for non-interacting fields. In the rest of my lectures, I will discuss several toy models in 1+1 and 3+1 dimensions and discuss how effective light-front Hamiltonians resolve the apparent paradox that results from having a trivial light-front …
Light-Front quantization is one of the most promising and physical tools towards studying deep inelastic scattering on the basis of quark gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum effects can only appear in zero-mode degrees of freedom) and the physical basis allows for a description of hadrons that stays close to intuition. I am reviewing recent progress in understanding the deep connection between renormalization of light-front Hamiltonians, effective light-front Hamiltonians and nontrivial vacuum condensates.
We investigate the leading-twist transverse momentum-dependent distribution functions (TMDs) for a physical electron, a spin-1/2 composite system consisting of a bare electron and a photon, using the Basis Light-front Quantization (BLFQ) framework. The light-front wave functions of the physical electron are obtained from the eigenvectors of the light-front QED Hamiltonian. We evaluate the TMDs using the overlaps of the light-front wave functions. The BLFQ results are found to be in excellent agreement with those TMDs calculated using lowest-order perturbation theory.
In this paper, we have calculated the lowest order splitting functions occurring in the Altarelli-Parisi equation in the light front hamiltonian formalism. Two component perturbative LFQCD in light cone gauge is our guideline and we have used LFTD-approximation for dressed quark and gluon states.
We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends-Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.
The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends-Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on…
We study the light-front covariance of a vector-meson decay constant using a manifestly covariant fermion field theory model in $(3+1)$ dimensions. The light-front zero-mode issues are analyzed in terms of polarization vectors and method of identifying the zero-mode operator and of obtaining the light-front covariant decay constant is discussed.
We identify an invariant light-front coordinate $ζ$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This frame-independent light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space. Light-front holography is a …
The definition of chiral transformations in light-front field theory is very different from the conventional form in equal-time formalism. We study the consistency of chiral transformations and chiral symmetry in light-front QCD and derive a complete new light-front axial-vector current for QCD. The breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new axial-vector current does not contain the pion pole part so that the associate chiral charge smoothly describes pion transitions for various hadronic proce…
We discuss the light-front zero-mode issue in the light-front quark model prediction of the twist-3 distribution amplitude of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD.
We present a calculation of Wigner distributions for gluons in light-front dressed quark model. We calculate the kinetic and canonical gluon orbital angular momentum and spin-orbit correlation of the gluons in this model.
In this series of lectures, I shall begin with the current investigations on phenomenology of hadron dynamics to demonstrate the importance of solving hadronic bound states within the framework of light-front (LF) QCD. Then, I will describe the basic procedure how to formulate the canonical theory of LFQCD, including light-front quantization of QCD, light-front gauge singularity, and light-front two-component formalism. I will also present a complete one-loop QCD calculation in terms of the light-front time-ordering perturbation theory, in comparison with the usual covariant perturbative QCD c…
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from the holographic soft-wall model.
The light-front quantization of QCD provides an alternative to lattice gauge theory for computing the mass spectrum, scattering amplitudes, and other physical properties of hadrons directly in Minkowski space. Nonperturbative light-front methods for solving gauge theory and obtaining light-front wavefunctions, such as discretized light-front quantization, the transverse lattice, and light-front resolvents are reviewed. The resulting light-front wavefunctions give a frame-independent interpolation between hadrons and their quark and gluon degrees of freedom, including an exact representation of…
We present the leading-twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 target, such as the $ρ$-meson, in the light-front framework. Specifically, we predict the TMDs in the light-front holographic model and compare with the light-front quark model predictions. We obtain the TMDs using the overlap of the light-front wave functions. We evaluate the ${\bf k}_\perp$ moments upto second order and compare with the available theoretical predictions. Further, we analyze the leading-twist parton distribution functions (PDFs) of the $ρ$-meson in the light-fr…
The light-front QCD is studied using the method of flow equations. Solving the light-front gluon gap equation, the effective gluon mass is generated dynamically. The effective interaction between static quark and antiquark, generated through elimination of the quark-gluon minimal coupling by flow equations, has the Coulomb, $1/q^2$, and confining, $1/q^4$, singular behavior. Elimination of the quark-gluon coupling at small gluon momenta is governed by the cutoff dependent, dynamical gluon mass, which makes this elimination possible and provides such an enhancement at $q\sim 0$. The cutoff, whi…
We show that Mellin moments of generalized parton distributions, given as even polynomials in the skewness parameter, are obtained from the Taylor expansion of light front wave functions. Furthermore, we derive non-standard versions of the inverse Radon transform to obtain the double distribution from the parton number conserved light front wave function overlap. These transformations are utilized to extend a generalized parton distribution from the outer region to the central one. We exemplify the formalism for a light front wave function that arises from an AdS/QCD duality conjecture.
We investigate the electroweak form factors and semileptonic decay rates of mesons using the constituent quark model based on the light-front degrees of freedom. Our results demonstrate the broader applicability of light-front approach including the timelike region of exclusive processes.
The light-front wavefunction for mesons predicted by holographic light-front QCD is used to obtain the light-cone distribution amplitudes for the light vector mesons and the transition form factors for B and $B_s$ decays to $ρ$, $K^*$ and $ϕ$ mesons. Here, I present some of our predictions as compared to lattice QCD, OCD sum rules and the available experimental data.
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.
The light-front approach is a relativistic quark model and offers many insights to the internal structures of the hadronic bound states. In this study, we apply the covariant light-front approach to ground-state heavy quarkonium. The pesudoscalar and vector meson decay constants are discussed. We present a detailed study of two-photon annihilation P \to γγand magnetic dipole transition V \to P γprocesses. The numerical predictions of the light-front approach are consistent with the experimental data and those in other approaches. The relations of the light-front approach with the other methods…
Numerical results for the calculation of the (rest-frame) $Q\bar{Q}$ potential, for light-front quantized $QCD_{2+1}$ on a $\perp$ lattice are presented. Both in the longitudinal as well as the $\perp$ spatial directions one obtains linear confinement. The resulting potential is almost rotational symmetric.
We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the…
We present model predictions of Collins asymmetries for proton in the SIDIS process for $π^+$ and $π^-$ channels. We use a recently proposed light-front quark-diquark model for proton with the light-front wave functions predicted in soft-wall AdS/QCD. The model predictions are compared with the HERMES and COMPASS data.
A recent paper by Alves, Das, and Perez contains a calculation of the one-loop self-energy in ϕ^{3} field theory at T\neq 0 using light-front quantization and concludes that the self-energy is different than the conventional answer and is not rotationally invariant. The changes of variables displayed below show that despite the complicated appearance of the thermal self-energy in light-front variables, it is exactly the same as the conventional result.
Basis Light-front Quantization (BLFQ) has recently been developed as a promising nonperturbative technique. Using BLFQ, we investigate the Generalized Parton Distributions (GPDs) in a nonperturbative framework for a dressed electron in QED. We evaluate light-front wave functions and carry out overlap calculations to obtain GPDs. We also perform perturbative calculations in the corresponding basis spaces to demonstrate that they compare reasonably with the BLFQ results.
We explore the deep inelastic structure functions of hadrons nonperturbatively in an inverse power expansion of the light-front energy of the probe in the framework of light-front QCD. We arrive at the general expressions for various structure functions as the Fourier transform of matrix elements of different components of bilocal vector and axial vector currents on the light-front in a straightforward manner. The complexities of the structure functions are mainly carried by the multi-parton wave functions of the hadrons, while, the bilocal currents have a dynamically dependent yet simple stru…
We derive the lowest-order $q\bar q$ valence light-front wave function for the pion with Lz=0 and |Lz|=1, which reproduces its valence parton distribution and the electromagnetic form factor consistent with data.
The kaon electromagnetic form factor is calculated within a light-front constituent quark model (LFCQM). The electromagnetic components of the current are extracted from the Feynman triangle diagram within the light-front approach. We also obtain the electroweak decay constant and the charge radius for the kaon in the light-front approach. In this work, the kaon observables are calculated and a fairly good agreement is obtained with a very higher accuracy when compared with the experimental data.
After reviewing a connection between quantum chromodynamics and contituent quark model pictures in the light-front quantization with some comparison and contrast to the ordinary equal-time bridge a la Bogoliubov-Valatin transformation, we discuss some newer development of the light-front quark model phenomenology in exclusive processes including the embedded state. The skewed parton distribution appears to be a good testing ground for our new effective treatment of the light-front nonvalence contributions in timelike exclusive processes.
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched s…
We discuss a relation between the light-front quark model and QCD. We argue that this model can be used for an evaluation of the light-cone wave functions for moderate values of "u", but that it is inapplicable for this purpose in the region near the ends points u=0,1. We find additional support for a recent analysis in which it was claimed that the twist-two pion wave function attains its asymptotic form. The asymptotic twist-four two-particle wave function is also in good agreement with the light-front quark model.
We consider the light-front holographic QCD with the light-front wave functions for mesons, modified for massive quarks. We evaluate the wave functions, distribution amplitudes, and form factors for $π$, $ρ$, $K$, and $J/ψ$ mesons and photon-to-meson transition form factors for $π$, $η$, and $η^\prime$ mesons. The results are compared with the experimental data, wherever available.
We incorporate the perturbative evolution effects in the generalized parton distributions (GPDs) calculated in effective light-front quark model for the nucleon. The perturbative effects enters into formalism through the evolution of GPDs according to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-like (DGLAP) equation. We obtain the evolved GPDs in the momentum space and transverse impact parameter space. We observe that combining the light front quark model with the perturbative evolution effects, give the effective model for studying the phenomenological GPDs
We propose a six-dimensional light-front Wigner distribution for the complete description of partonic structures of a hadron such as pion and proton, taking advantage of the recently proposed light-front variable $\tilde{z}$ by Miller and Brodsky. Quantities derived from the Wigner distribution contain the most general information of partonic structures, including also new quantities correlating longitudinal coordinate with transverse momenta or transverse coordinates, together with spins. The new Wigner distribution can be viewed as a relativistic version of the original Wigner distribution i…
The spin asymmetries in SIDIS associated with $T$-odd TMDs are presented in a light-front quark-diquark model of a proton. To incorporate the effects of the final state interaction, the light front wave functions are modified to have a phase factor which is essential to have Sivers or Boer-Mulders functions. The Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.
Using global fits of valence u and d quark parton distributions and data on quark and nucleon form factors in the Euclidean region, we derive a light-front quark model for the nucleon structure consistent with quark counting rules.
The charge and transition form factors of pion ($F_π$, $F_{πγ}$, and $F_{πγ^*}$) are studied with the light-front quark model. We find that our results for $F_π$ and $F_{πγ}$ agree very well with experimental data. Furthermore, the decay constants of $η$ and $η'$ are evaluated. We also calculate $F_{ηγ}$ and $F_{η'γ}$ and compare with the experimental data.
We present the Poincare algebra interpolating between instant and light-front time quantizations. The angular momentum operators satisfying SU(2) algebra are constructed in an arbitrary interpolation angle and shown to be identical to the ordinary angular momentum and Leutwyler-Stern angular momentum in the instant and light-front quantization limits, respectively. The exchange of the dynamical role between the transverse angular mometum and the boost operators is manifest in our newly constructed algebra.
Using light-front holography, we predict simultaneously the pion decay constant and the pion charge radius by taking into account (higher twist) dynamical spin effects whose relative importance is constrained by QCD.
We examine the light-front zero-mode contribution to the good(+) current matrix elements between pseudoscalar and vector mesons. In particular, we discuss the transition form factor $f(q^2)$ which has been suspected to have the light-front zero-mode contribution. While the zero-mode contribution in principle depends on the form of the vector meson vertex $Γ^μ=γ^μ- (P_V -2k)^μ/D$, the form factor $f(q^2)$ is found to be free from the zero-mode contribution if the denominator $D$ contains the term proportional to the light-front energy $(k^-)^{n}$ with the power $n>0$. The lack of zero-mode cont…
Decay constants and form factors for parity-even (s-wave) and parity-odd (p-wave) mesons are studied within a covariant light-front approach. The three universal Isgur-Wise functions for heavy-to-heavy meson transitions are obtained.
We report that the pion radius, decay constant, EM and transition form factors can simultaneously and accurately be predicted in light-front holographic QCD with a universal AdS/QCD mass scale, provided dynamical spin effects are taken into account.
We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the fi…
Two methods for the nonperturbative solution of field-theoretic bound-state problems, based on light-front coordinates, are briefly reviewed. One uses Pauli-Villars regularization and the other supersymmetry. Applications to Yukawa theory and super Yang-Mills theory with fundamental matter are emphasized.
For the vector sector, i.e, mesons with spin-1, the electromagnetic form factors and anothers observables are calculated with the light-front approach. However, the light-front quantum field theory have some problems, for example, the rotational symmetry breaking. We solve that problem added the zero modes contribuition to the matrix elements of the electromagnetic current, besides the valence contribuition. We found that among the four independent matrix elements of the plus component in the light-front helicity basis only the $0\to 0$ one carries zero mode contributions.
In this article we review the basic formulation of light-front field theory and light-front phenomena in strong interaction. We also explore various approaches to the understanding of these phenomena and the associated problems of hadronic bound states based on QCD (quantum chromodynamics) on the light-front.
We study the radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach, and investigate the effects of using different current component and different reference frames. In practical calculations with truncated Fock spaces, transition form factors may acquire current component dependence and frame dependence, and such dependences could serve as a measure for the Lorentz symmetry violation. We suggest using the transverse current with $m_j=0$ state of the vector meson, since this procedure employs the dominant spin components of the light-front wavef…
The frame dependence of the pair-term contribution to the electromagnetic form factor of the pion is studied within the Light Front approach. A symmetric ansatz for the pion Bethe-Salpeter amplitude with a pseudo scalar coupling of the constituent to the pion field is used. In this model, the pair term vanishes for the Drell-Yan condition, while it is dominant for momentum transfer along the light-front direction.
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 fra…
