We solve for the $ρ$-meson's wave functions from a light-front QCD Hamiltonian determined for its constituent quark-antiquark and quark-antiquark-gluon Fock components, with a three-dimensional confinement using basis light-front quantization. From this, we obtain the leading-twist valence quark's parton distribution functions and transverse momentum-dependent parton distributions inside the $ρ$-meson. These results are qualitatively consistent with those of other models. We also demonstrate the important effects of a dynamical gluon on the $ρ$-meson's gluon densities, helicity, transversity, and tensor polarized distributions.
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.
The flow-equation method of continuous unitary transformations is used to eliminate the minimal quark-gluon interaction in the light-front quantized QCD Hamiltonian. The coupled differential equations in the two lowest Fock sectors correspond to the renormalization of the light-front gluon mass and the generation of an effective quark-antiquark (as well as gluon-gluon) interaction. The original gauge field coupling is completely eliminated, even in the presence of degenerate states connected by this interaction. Further, a more singular $1/q^4$ behavior for the quark and gluon effective intera…
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.
We have scrutinized the transverse momentum dependent quark-gluon-quark correlation function. We have utilized the light-front quark-diquark model to study the time-reversal-odd interaction-dependent twist-3 gluon distributions which we have obtained from the disintegration of the transverse momentum dependent quark-gluon-quark correlator. Specifically, we have studied the behavior of $\tilde{e}_{L}$ and $\tilde{e}_{T}$ while considering our diquark to be an axial-vector.
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.
We investigate the tree level multi-gluon components of the gluon light cone wavefunctions in the light cone gauge keeping the exact kinematics of the gluon emissions. We focus on the components with all helicities identical to the helicity of the incoming gluon. The recurrence relations for the gluon wavefunctions are derived. In the case when the virtuality of the incoming gluon is neglected the exact form of the multi-gluon wavefunction as well as the fragmentation function is obtained. Furthermore we analyze the 2 to N tree-level gluon scattering in the framework of light-front perturbatio…
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…
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.
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…
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.
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
A constituent parton picture of hadrons with logarithmic confinement arises naturally in light-front QCD when the hamiltonian is computed using a perturbative renormalization group; however, rotational symmetry is not manifest as a simple kinematic symmetry. Relevant operators must typically be fine-tuned when a perturbative renormalization group is used, and in light-front field theory such operators contain functions of longitudinal momenta. We explore the possibility that a gluon mass operator with simple longitudinal momentum dependence may improve approximate kinematic rotational symmetry…
We investigate the electromagnetic form factors of the nucleon in the framework of basis light front quantization. We compute the form factors using the light front wavefunctions obtained by diagonalizing the effective Hamiltonian consisting of the holographic QCD confinement potential, the longitudinal confinement, and a one-gluon exchange interaction with fixed coupling. The electromagnetic radii of the nucleon are also computed.
Solving instability of Savvidy vacuum in QCD is a longstanding problem. Using light cone quantization we analyze the problem not in the real confining vacuum but in dense quark matter where gluons interact weakly with each other. We find a stable ferromagnetic ground state of gluons which carry a single longitudinal momentum. Their states are composed as if they are confined in a two dimensional quantum well. This supports our previous result that gluons form a quantum Hall state in dense quark matter.
We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with focus on correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering (DPS) in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results gives insight to the strengths of correlations in different kinematical regions, which can help in constructing input DPDs in cro…
We compute the structure function, transverse momentum dependent parton distributions (TMDs), and generalized parton distributions (GPDs) for the physical photon from the light-front quantum electrodynamics (QED) Hamiltonian, determined for its constituent bare photon and electron-positron Fock components within the Basis Light-Front Quantization framework. After performing nonperturbative renormalization, we obtain a good quality description of the perturbative QED properties of the photon, as well as good agreement with the experimental data for the photon's structure function. We also inves…
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 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 obtain the light-front wavefunctions for the nucleon in the valence quark Fock space from an effective Hamiltonian, which includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling. The wavefunctions are generated by solving the eigenvalue equation in a basis light-front quantization. Fitting the model parameters, the wavefunctions lead to good simultaneous description of electromagnetic form factors, radii, and parton distribution functions for the proton.
As implied by organizers, this talk is not a conference summary but rather an outline of progress/challenges/``frontiers'' of the theory. Some fundamental questions addressed are: Why is sQGP such a good liquid? Do we understand (de)confinement and what do we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical ``gravity dual'' to heavy ion collisions?
We introduce a new method to include condensates in the light-cone Hamiltonian. By using a Gaussian approximation to the ordinary vacuum in a theory close to the light front, we derive an effective Hamiltonian on the light cone, which has new terms reflecting the nontriviality of the vacuum. We demonstrate our method for scalar $ϕ^4$-theory and the massive Schwinger model.
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) 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 consist…
We study the unpolarized and the helicity dependent generalized parton distributions (GPDs) for the valence quarks of the proton in both momentum space and position space within the basis light-front quantization (BLFQ) framework. The GPDs for the valence quarks are computed from the eigenvectors of a light-front effective Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. Employing these GPDs, we obtain the spatial distributions of quark angular momentum inside the proton. In our BLFQ approac…
Flow equations method of continuous unitary transformations is used to eliminate the minimal quark-gluon interaction in the light-front quantized QCD Hamiltonian. The coupled differential equations in the two lowest Fock sectors correspond to the renormalization of the light-front gluon mass and the generation of effective quark-antiquark interaction. The influence of the renormalization of the gluon effective mass on the elimination of the quark-gluon coupling and the induced quark-antiquark interaction is taken into account. Namely, the original gauge field coupling can be completely elimina…
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…
Dynamical gluon effects in proton transversity and off-forward parton distributions from a light-front Hamiltonian approach
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Iowa State University（爱荷华州立大学）
The effect of a sharp front separating the quark-gluon plasma phase from the hadronic phase is investigated. Energy-momentum conservation and baryon number conservation constrain the possible temperature jump across the front. If one assumes that the temperature in the hadronic phase is $T\simeq$ 200 MeV , as has been suggested by numerous results from relativistic ion collisions, one can determine the corresponding temperature in the quark phase with the help of continuity equations across the front. The calculations reveal that the quark phase must be in a strongly supercooled state. The sta…
We investigate the structure of the light meson with one dynamical gluon from the light-front QCD Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock sectors, together with a three-dimensional confinement. After fitting the light meson mass spectroscopy, the light-front wave functions provide a good quality description of the pion electromagnetic form factor, and the valence quark distribution functions following QCD scale evolution.
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time cannot be transformed into each other. While they would thus appear to describe different theories, we show that this is not in fact the case. In instant-time quantization unequal instant-time commutation or anticommutation relations for free scalar, fermion, or gauge boson fields are c-numbers. We show that when these unequal instant-time commutation or anticommutation relations are evaluated at equal light-front time they are identical to t…
We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the rest…
The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor $g_{\bar{μν}}$ is non-diagonal. The Kubo, Martin, Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount $-i\big/(T\sqrt{g_{\bar{00}}})$. Light front quantization fails since $g_{\bar{00}}=0$, however various related quantizations are possible.
It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy b…
It is often stated that the vacuum is trivial when light-front (null-plane) quantization is applied to a quantum field theory, in contrast to the situation with equal-time quantization. In fact, it is has long been known that the statement is false, and that in certain cases the standard rules for light-front perturbation theory need modification. This paper gives an elementary review of these issues, including an explanation of how and when there is a failure of the elementary derivation of the rules for light-front perturbation theory.
Basis Light-front Quantization has been developed as a first-principles nonperturbative approach to quantum field theory. In this article we report our recent progress on the applications to the single electron and the positronium system in QED. We focus on the renormalization procedure in this method.
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 th…
We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extens…
While the particle-number-conserving convolution formalism established in the Drell-Yan-West reference frame is frequently used to compute exclusive amplitudes in the light-front quantization, this formalism is limited to only those frames where the light-front helicities are not changed and the good (plus) component of the current remains unmixed. For an explicit demonstration of such criteria, we present the relations between the current matrix elements in the two typical reference frames used for calculations of the exclusive amplitudes, i.e. the Drell-Yan-West and Breit frames and investig…
We present a calculation of the mass spectrum of positronium within the framework of the recently developed Basis Light-Front Quantization approach to non-perturbative quantum field theory. In this calculation, we employ a two-body effective interaction for the photon exchange, neglecting self-energy effects. We demonstrate the cancellation of Light-Front small-{\it x} divergences within our non-perturbative approach. The resulting spectrum is compared to both non-relativistic quantum mechanics and previous work in Discretized Light-Cone Quantization.
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 ultra-violet 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 renormali…
We employ an effective Hamiltonian that includes the transverse and longitudinal confinement and the one-gluon exchange interaction with fixed coupling constant. By solving the eigenvalue equation in basis light-front quantization (BLFQ), we generate the light-front wavefunctions (LFWFs) for the nucleon in the valence quark Fock space. Fitting the model parameters, we obtain high-quality descriptions of electromagnetic form factors and radius for proton while the results deviate somewhat from experimental data for neutron.
We propose a mechanism which naturally contains the relation $μ_{B} = 3μ_{S}$ of the hadronic gas produced in heavy-ion collisions at CERN. Our starting assumption is the existence of a sharp front separating the quark-gluon plasma phase from the hadronic phase. Energy-momentum conservation across the front leads to the following consequences for an adiabatic process a) The baryon chemical potential, $μ_{B}$, is approximately continuous across the front. b) The temperature in the hadronic gas is higher than the phase transition temperature due to superheating. c) In the region covered by the e…
We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pion's gluon densities can be probed through the pion-nucleus induced $J/ψ$ production data. Our pion part…
The contribution of crossed gluon fields in flux tubes connecting quarks to the proton spin is calculated. The calculations are performed following non-perturbative Heisenberg's quantization technique. In our approach a proton is considered as consisting of three quarks connected by three flux tubes. The flux tubes contain color longitudinal electric and transversal electric and magnetic fields. The transversal fields causes the appearance of the angular momentum density. The dimensionless relation between the angular momentum and the mass of the gluon fields is obtained. The contribution to p…
Basis Light-front Quantization (BLFQ) is a nonperturbative approach to quantum field theory. In this paper, we report our recent progress in applying BLFQ to the positronium system in QED and to the meson and the baryon system in QCD. We present preliminary results on the mass spectrum, light-front wave functions and other observables of these systems, where one dynamical gauge boson is retained for the positronium and meson systems.
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time not only cannot be transformed into each other, they take completely different forms. While they would thus appear to describe different theories, we show that this is not in fact the case. By looking not at equal times but at unequal times, we show that unequal instant-time commutation or anticommutation relations are completely equivalent to unequal light-front time commutation or anticommutation relations. Light-front quantization and inst…
We consider the transverse momentum dependent gluon distribution functions (called gluon TMDs) by studying the light-front gluon-gluon correlator, extending the results for unpolarized and vector polarized targets to also include tensor polarized targets -- the latter type of polarization is relevant for targets of spin $\ge1$. The light-front correlator includes process-dependent gauge links to guarantee color gauge invariance. As from the experimental side the gluon TMDs are largely unknown, we present positivity bounds for combinations of leading-twist gluon distributions that may be used t…
