A. Harindranath

Nonperturbative QCD: A weak-coupling treatment on the light front.

In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the Constituent Quark Model with the complexities of Quantum Chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses, which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.

Hamiltonian light-front field theory in a basis function approach

Hamiltonian light-front quantum field theory constitutes a framework for the nonperturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories is obtained that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present illustrative features of some noninteracting systems in a cavity. We illustrate the first steps toward solving quantum electrodynamics (QED) by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.

Orbital angular momentum in deep inelastic scattering

In this work we address several issues associated with the orbital angular momentum relevant for leading twist polarized deep inelastic scattering. We present a detailed analysis of the light-front helicity operator (generator of rotations in the transverse plane) in QCD. We explicitly show that the operator constructed from the manifestly gauge invariant, symmetric energy momentum tensor in QCD, in the gauge

Hadron optics: Diffraction patterns in deeply virtual Compton scattering

{A}^{+}=0,

Ab initio results for the broken phase of scalar light front field theory

after the elimination of constraint variables, is equal to the naive canonical form of the light-front helicity operator plus surface terms. Restricting to the topologically trivial sector, we eliminate the residual gauge degrees of freedom and surface terms. Having constructed the gauge fixed light-front helicity operator, we introduce quark and gluon orbital helicity distribution functions relevant for polarized deep inelastic scattering as a Fourier transform of the forward hadron matrix elements of appropriate bilocal operators. The utility of these definitions is illustrated with the calculation of anomalous dimensions in perturbation theory. We explicitly verify the helicity sum rule for dressed quark and gluon targets in light-front perturbation theory. We also consider the internal orbital helicity of a composite system in an arbitrary reference frame and contrast the results in the nonrelativistic situation versus the light-front (relativistic) case.

Kinks in discrete light cone quantization

We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable {zeta} provides a unique way to visualize the light-front wavefunctions (LFWFs) of the target state in the boost-invariant longitudinal coordinate space variable ({sigma} = P{sup +}y{sup -}/2). The results are analogous to the diffractive scattering of a wave in optics in which the dependence of the amplitude on {sigma} measures the physical size of the scattering center of a one-dimensional system. If one combines this longitudinal transform with the Fourier transform of the DVCS amplitude with respect to the transverse momentum transfer {Delta}{sup {perpendicular}}, one can obtain a complete three-dimensional description of hadron optics at fixed light-front time {tau} = t + z/c. As a specific example, we utilize the quantum fluctuations of a fermion state at one loop in QED to obtain the behavior of the DVCS amplitude for electron-photon scattering. We then simulate the wavefunctions for a hadron by differentiating the above LFWFs with respect to M{sup 2} and study the corresponding DVCS amplitudes in {sigma} space.

Transition in the spectrum of the topological sector of {phi}{sub 2}{sup 4} theory at strong coupling

Abstract We present nonperturbative light-front energy eigenstates in the broken phase of a two-dimensional λ 4 ! ϕ 4 quantum field theory using discrete light cone quantization and extrapolate the results to the continuum limit. We establish degeneracy in the even and odd particle sectors and extract the masses of the lowest two states and the vacuum energy density for λ = 0.5 and 1.0. We present two novel results: the Fourier transform of the form factor of the lowest excitation as well as the number density of elementary constituents of that state. A coherent state with kink–antikink structure is revealed.

Deep inelastic structure functions in light-front QCD: Radiative corrections

Abstract We investigate non-trivial topological structures in discrete light cone quantization (DLCQ) through the example of the broken symmetry phase of the two-dimensional φ4 theory using antiperiodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi-classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.

On transverse spin sum rules

We investigate the strong coupling region of the topological sector of the two-dimensional {phi}{sup 4} theory. Using discrete light cone quantization, we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered {phi}{sup 2} operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional {phi}{sup 4} theory.

Light-front QCD. I. Role of longitudinal boundary integrals.

Recently, we have introduced a unified theory to deal with perturbative and non-perturbative QCD contributions to hadronic structure functions in deep inelastic scattering. This formulation is realized by combining the coordinate space approach based on light-front current algebra techniques and the momentum space approach based on Fock space expansion methods in the Hamiltonian formalism of light-front field theory. In this work we show how a perturbative analysis in the light-front Hamiltonian formalism leads to the factorization scheme we have proposed recently. The analysis also shows that the scaling violations due to perturbative QCD corrections can be rather easily addressed in this framework by simply replacing the hadron target by dressed parton target and then carrying out a systematic expansion in the coupling constant