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We illustrate, in a semi-classical picture, how the Wilson line phase factor in gauge invariantly defined unintegrated parton density can lead to a nonzero single-spin asymmetry (Sivers effect)., Comment: 6 pages, invited talk given at "QCD Down Under 2004", and "Continuous Advances in QCD 2004"

We study T-odd gauge invariantly defined T-odd unintegrated gluon densities in QCD. The average $\perp$ momentum of the gluons in a $\perp$ polarized nucleon can be nonzero due to the Sivers mechanism. However, we find that the sum of the transverse momenta due to the Sivers mechanism from gluons and all quark flavors combined vanishes, i.e. $<{\bf k_{\perp,g}}> + \sum_q < {\bf k_{\perp,q}}> =0$., Comment: 4 pages, 1 figure, revtex

The $t$-dependence of generalized parton distrbutions for $x\to 1$ is discussed. We argue that constituent quark models, where the $t$-dependence for $x\to 1$ is through the product $(1-x)t$, are inconsistent. Instead we suggest a leading dependence in terms of $(1-x)^n t$, where $n\geq 2$, for $x\to 1$., Comment: 4 pages, revtex

The relation between GPD's and color transparency is explored. The discovery of color transparency in pionic diffractive dissociation reactions allows us to make specific predictions for the behavior of the pion generalized parton distribution, and provide a further test of any model of the pion form factor., Comment: 12 pages, 3 figures

We analyze the Sivers asymmetry in light-cone gauge. The average transverse momentum of the quark distribution is related to the correlation between the quark distribution and the transverse component of the gauge field at $x^-\pm \infty$. We then use finiteness conditions for the light-cone Hamiltonian to relate the transverse gauge field at $x^-=\pm \infty$ to the color density integrated over $x^-$. This result allows us to relate the average transverse momentum of the active quark to color charge correlations in the transverse plane., Comment: 8 pages, 1 figure

The physical interpretation of generalized parton distributions (in the limit $\xi=0$) as Fourier transforms of impact parameter dependent parton distributions is discussed. Particular emphasis is put on the role of the target polarization. For transversely polarized targets we expect a significant deviation from axial symmetry for the distribution in the transverse plane. We conjecture that this transverse distortion, in combination with the final state provides a natural explanation for the sign of the Sivers contribution to semi-inclusive single-spin asymmetries., Comment: 8 pages, invited talk given at workshop on `light-cone 2003: Hadrons and Beyond' (Durham, August 2003) and at `NAPP 2003' (Dubrovnik, Croatia, May 2003)

We discuss some constraints on the $x$ and $t$-dependence of $E(x,0,t)$ that arise from positivity bounds in the impact parameter representation. In addition, we show that $E(x,0,0)$ for the nucleon vanishes for $x\to 1$ at least as rapidly as $(1-x)^4$. Finally we provide an inequality that limits the contribution from $E$ to the angular momentum sum rule., Comment: 3 pages

Recently, it has been pointed out that there exists a connection between the generalized parton distribution $E(x,0,t)$ and the Sivers asymmetry. For transversely polarized nucleon targets, generalized parton distributions are asymmetric in impact parameter space. This impact parameter space asymmetry, together with the final state interaction of the active quark, gives rise to the Sivers asymmetry in momentum space. We demonstrate this phenomenon explicitly in the scalar diquark model. This result also illustrates the physics that underlies the correlation between the anomalous magnetic moment and the Sivers asymmetry for a given quark flavor., Comment: 16 pages, typos corrected

We illustrate how an axial asymmetry in impact parameter dependent parton distributions can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. The single spin asymmetry arising from the asymmetry of the impact parameter dependent parton distributions is shown to exhibit a pure $\sin \phi$ dependence., Comment: 6 pages

Generalized parton distributions (GPDs) with purely transverse momentum transfer can be interpreted as Fourier transforms of the distribution of partons in impact parameter space. The helicity-flip GPD $E(x,0,-\Dps)$ is related to the distortion of parton distribution functions in impact parameter space if the target is not a helicity eigenstate, but has some transverse polarization. This transverse distortion can be used to develop an intuitive explanation for various transverse single spin asymmetries., Comment: revised version, to appear in PRD

The Fourier transform of generalized parton distribution functions at xi=0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to the impact parameter distribution of unpolarized quarks for an unpolarized nucleon, H-tilde is related to the distribution of longitudinally polarized quarks in a longitudinally polarized nucleon, and $E$ is related to the distortion of the unpolarized quark distribution in the transverse plane when the nucleon has transverse polarization., Comment: addtl. corrections, 34 pages

For an unpolarized target, the generalized parton distribution $H_q(x,0,t)$ is related to the distribution of partons in impact parameter space. The transverse distortion of this distribution for a transversely polarized target is described by $E_q(x,0,t)$., Comment: 6 pages, espcrc1.sty, invited talk, QCDN'02, Ferrara, April 2002

We study how the components of hadronic wave functions in light-cone quantization depend on the ultraviolet cut-off by relating them in a systematic way to the matrix elements of a class of quark-gluon operators between the QCD vacuum and the hadrons. From this, we derive an infinite set of scale-evolution equations for the individual contributions to parton distributions from the Fock expansion. When summed over all the contributions, we recover the well-known DGLAP equation., Comment: 9 pages, references added

To appear in the proceedings of The Phenomenology of Large N(c) QCD, Tempe, Arizona, 9-11 Jan 2002., Comment: 5 pages, 2 figures, other comments

Chiral condensates in the trivial light-cone vacuum emerge if defined as short-time limits of fermion propagators. In gauge theories, the necessary inclusion of a gauge string in combination with the characteristic light-cone infrared singularities contain the relevant non-perturbative ingredients responsible for formation of the condensate, as demonstrated for the 't Hooft model., Comment: 4 pages, Revtex4

The formalism for describing hadrons using a light-cone Hamiltonian of SU(N) gauge theory on a coarse transverse lattice is reviewed. Physical gauge degrees of freedom are represented by disordered flux fields on the links of the lattice. A renormalised light-cone Hamiltonian is obtained by making a colour-dielectric expansion for the link-field interactions. Parameters in the Hamiltonian are renormalised non-perturbatively by seeking regions in parameter space with enhanced Lorentz symmetry. In the case of pure gauge theories to lowest non-trivial order of the colour-dielectric expansion, this is sufficient to determine accurately all parameters in the large-N limit. We summarize results from applications to glueballs. After quarks are added, the Hamiltonian and Hilbert space are expanded in both dynamical fermion and link fields. Lorentz and chiral symmetry are not sufficient to accurately determine all parameters to lowest non-trivial order of these expansions. However, Lorentz symmetry and one phenomenological input, a chiral symmetry breaking scale, are enough to fix all parameters unambiguously. Applications to light-light and heavy-light mesons are described., Comment: 55 pp, revised version, to appear in `Progress in Particle and Nuclear Physics'

I discuss the physical interpretation of GPDs in the limit $\xi=0$, where the $t$ dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also provides a physical interpretation for Ji's angular momentum sum rule., Comment: invited talk at `Workshop on Lepton Scattering, Hadrons and QCD', Adelaide, March 26 - April 6, 2001, 8 pages, sprocl.sty

We present results from a study of meson spectra and structure in the limit where one quark is infinitely heavy. The calculations, based on the framework of light-front QCD formulated on a transverse lattice, are the first non-perturbative studies of B-mesons in light-front QCD. We calculate the Isgur-Wise form factor, light-cone distribution amplitude, the heavy-quark parton distribution function and the leptonic decay constant of B-mesons., Comment: 5 pages, 3 figures, Revtex, corrected typos, added references, included moments

Generalized parton distributions (GPDs) provide a link between form factors, parton distributions and other observables. I discuss the connection between GPDs and parton distributions as a function of the impact parameter. Since this connection involves GPDs in the limit of vanishing skewedness parameter $\xi$, i.e. when the off-forwardness is purely transverse, I also illustrate how to relate $\xi\neq 0$ data to $\xi=0$ data, which is important for experimental measurements of these observables., Comment: 5 pages, to appear in: proceedings of the Second Workshop on Physics with a Polarized-Electron Light-ion Collider (EPIC), Cambridge, MA, Sept. 14-16, 2000

The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $\zeta$, i.e. when the off-forwardness is purely transverse. For the $2^{nd}$ moment it is also illustrated how to relate $\zeta\neq 0$ data to $\zeta=0$ data, which is important for experimental measurements of these observables., Comment: invited talk presented at `Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology', Heidelberg, June 2000, 10 pages, elsart.sty

We present a number of exact relations for the heavy quark limit and develop an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the new results are relation 3\mu_\pi^2=\bar\Lambda^2 - m_{sp}^2+\beta^2, 1/m_Q corrections to the decay constants, to the kinetic expectation values and 1/m_Q^2 nonperturbative corrections to the B->D amplitude at zero recoil. The properties of the IW functions are addressed and the small velocity sum rules are verified., Comment: 22 pages, plain LaTeX (no figures)

We use two-dimensional QCD as a toy laboratory to study off-forward parton distributions (OFPDs) in a covariant field theory. Exact expressions (to leading order in $1/N_C$) are presented for OFPDs in this model and are evaluated for some specific numerical examples. Special emphasis is put on comparing the $x>\zeta$ and $x<\zeta$ regimes as well as on analyzing the implications for the light-cone description of form factors., Comment: Revtex, 6 pages, 4 figures

It is shown that off-forward parton distributions for $\zeta =0$, i.e. where the initial and final state differ only in their transverse momenta, can be interpreted as a simultaneous measurement of the longitudinal momentum and transverse position (impact parameter) of partons in the infinite momentum frame., Comment: 5 pages, REVTEX

In these notes, the transverse ($\perp$) lattice approach is presented as a means to control the $k^+\to 0$ divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the $\perp$ lattice motivate the color-dielectric formulation, where the link fields are linearized., Comment: 7 pages, aipproc.sty, invited talk presented at 11th International Light-Cone School and Workshop: New Directions in Quantum Chromodynamics, Seoul, Korea, 26 May - 26 Jun 1999 & 12th Nuclear Physics Summer School and Symposium

The $Q\bar{Q}$ potential is calculated in the Color-Dielectric Formulation of Transverse Lattice QCD. In such a formulation an effective potential is used to enforce the $SU(N_c)$ symmetry of the link fields. This effective potential is truncated at fourth order. Surprisingly, there is striking rotational invariance in the ground state $Q\bar{Q}$ potential as well as in the first hybrid mode., Comment: Talk given at ``Quark Confinement and the hadron spectrum III'', Newport News, VA, June 1998; 4 pages, 3 figures, worldsci.sty

Naively, helicity flip amplitudes for fermions seem to vanish in the chiral limit of light-front QCD, which would make it nearly impossible to generate a small pion mass in this framework. Using a simple model, it is illustrated how a large helicity flip amplitude is generated dynamically by summing over an infinite number of Fock space components. While the kinetic mass is basically generated by a zero-mode induced counter-term, the vertex mass is generated dynamically by infinitesimally small, but nonzero, momenta. Implications for the renormalization of light-front Hamiltonians for fermions are discussed.

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 vacuum., Comment: 30 pages, lecture notes based on three lectures given at the NUclear Summer School NUSS 97, at Seoul National University, Seoul, South Korea, May 1997

A phenomenological model for the quark structure of mesons is considered. The model is based on the tube model for QCD, where all quanta with nonzero transverse momenta are neglected. In the limit that the mass term of the gluons goes to infinity, the model is equivalent to a combination of the 't Hooft and Gross-Neveu models and can be solved semi-analytically. The model has the properties of confinement, chiral symmetry breaking and asymptotic freedom and thus resembles QCD in three key respects. Spectra, distribution amplitudes and form factors of mesons are analyzed., Comment: final version, to appear in PRD

In the context of simple models, it is shown that demanding finiteness for physical masses with respect to a longitudinal cutoff, can be used to fix the ambiguity in the renormalization of fermions masses in the Hamiltonian light-front formulation. Difficulties that arise in applications of finiteness conditions to discrete light-cone quantization are discussed., Comment: REVTEX, 9 pages

Numerical results for the (rest-frame) $Q\bar{Q}$ potential in 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 confinement mechanism in light-front QCD depends on the orientation of the external charges: for longitudinally (with respect to the boost direction in the infinite momentum frame) separated quarks, confinement arises from the instantaneous interaction piece in the Hamiltonian while for $\perp$ separated quarks, the confinement mechanism is similar to the one in Hamiltonian lattice QCD. Nevertheless, already a very simple ansatz for the effective link-field potential yields an almost rotationally symmetric $Q\bar{Q}$ potential. The momentum carried by the glue strongly depends on the orientation ("polarization") of the $Q\bar{Q}$ pair., Comment: Talk given at $3^{rd}$ AUP workshop on "Confinement, Chaos and Collision", Paris, France, June 96. Uses lprocl.sty

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., Comment: Contributed to PANIC96, LATEX (sprocl), 2 pages, 1 figure

The background-field formalism is used extensively in fundamental approaches to QCD to explore hadronic matrix elements of various currents. While the lattice QCD approach is formulated in the fully-interacting Hilbert space, which includes both QCD and background field interactions, the QCD sum-rule formalism is traditionally developed in the pure-QCD Hilbert space. The latter approach encounters difficulties with excited state contaminations which are not exponentially suppressed and requires extrapolations to isolate the desired physics. Proponents of the pure-QCD Hilbert space formalism used in the QCD sum-rule approach have criticized the lattice QCD approach as neglecting important physics. In this letter, the equivalence of the two approaches is established and the flaws in the former criticisms are resolved. Finally, the application of the fully-interacting Hilbert space formalism to the study of electromagnetic polarizabilities is outlined., Comment: 9 pages. Revised version accepted for publication. This and related papers may also be obtained from http://www.phys.washington.edu/~derek/Publications.html#LatticeQCD

In the light-front form of field theory, boost invariance is a manifest symmetry. On the downside, parity and rotational invariance are not manifest, leaving the possibility that approximations or incorrect renormalization might lead to violations of these symmetries for physical observables. In this paper, it is discussed how one can turn this deficiency into an advantage and utilize parity violations (or the absence thereof) in practice for constraining effective light-front Hamiltonians. More precisely, we will identify observables that are both sensitive to parity violations and easily calculable numerically in a non-perturbative framework and we will use these observables to constrain the finite part of non-covariant counter-terms in effective light-front Hamiltonians., Comment: REVTEX, 9 pages

We propose the tube model as a first step in solving the bound state problem in light-front QCD. In this approach we neglect transverse variations of the fields, producing a model with 1+1 dimensional dynamics. We then solve the two, three, and four particle sectors of the model for the case of pure glue SU(3). We study convergence to the continuum limit and various properties of the spectrum., Comment: 29 pages

The status of the transverse lattice formulation of light-front QCD is reviewed. It is explained how confinement arises in this formulation for large lattice spacing. The nonperturbative renormalization procedure is outlined in general and a more detailed discussion is given for the case of $QCD_{2+1}(N_C\rightarrow \infty)$., Comment: 5 pages, LATEX, 1 postscript figure

An introductory overview on Light-Front quantization, with some emphasis on recent achievements, is given. Light-Front quantization is the most promising and physical tool to study 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. Recent progress has ben made in understanding the connection between effective LF Hamiltonians and nontrivial vacuum condesates. Discrete Light-Cone Quantization, the transverse lattice and Light-Front Tamm-Dancoff (in combination with renormalization group techniques) are the main tools for exploring LF-Hamiltonians nonperturbatively., Comment: LATEX, 87 pages, postscript files for the figures or a postscript file for the complete article (900 kB) available from the author

Precise measurements of polarized electro-production and Drell-Yan in the deep inelastic limit will soon provide first information on the higher twist parton distributions $g_T(x)$ and $h_L(x)$. Sum rules for higher-twist structure functions are only valid provided the corresponding Compton amplitudes satisfy un-subtracted dispersion relations. Subtracted dispersion relations have to be used when the (real part of the) forward scattering amplitudes does not fall off rapidly enough for $\nu \rightarrow \infty$ (fixed $Q^2$). Formally, such subtractions lead to $\delta$-functions at the origin in the parton distributions, which are not accessible to experiment, and the integral over the data fails to satisfy the sum rule. The $\delta$-functions in the parton distributions can be identified with the zero-modes that appear in light-front quantization. An explicit {\it infinite momentum boost} identifies these soft quark modes with low momentum contributions to the self-energy., Comment: 12 pages, REVTEX, 5 figures as postscript files available from the Author

A scheme is developed which shows how one would, given a light-front Hamiltonian for QCD, extract the $Q\overline{Q}$ potential, i.e. the quantity which corresponds to the potential between two infinitely heavy quarks in a rest frame, from a light-front calculation. The resulting potential will in general depend on the direction along which the infinitely heavy sources are separated and thus provides a direct probe of violations of rotational invariance in a physical observable. Furthermore, easy comparison to data from $c\overline{c}$ and $b\overline{b}$ spectroscopy and to lattice data is possible. The scheme may thus be very helpful in constructing a light-front Hamiltonian through an iterative procedure., Comment: 7 pages, LATEX

In the limit of an infinite number of colors, we derive an analytic expression for the quark condensate in $QCD_{1+1}$ as a function of the quark mass and the gauge coupling constant. For zero quark mass, a nonvanishing quark condensate is obtained. Nevertheless, we prove that there is no phase transition as a function of the quark mass. It is furthermore shown that the expansion of $\langle 0 | \overline{\psi}\psi |0\rangle$ in the gauge coupling has zero radius of convergence but that the perturbation series is Borel summable with finite radius of convergence. The nonanalytic behavior $\langle 0 | \overline{\psi}\psi |0\rangle \stackrel{m_q\rightarrow0}{\sim} - N_C \sqrt{G^2}$ can only be obtained by summing the perturbation series to infinite order., Comment: 5 pages, 1 postscript figure (available by email from the author), LATEX

We develop simple analytic representations of the polarized quark and gluon distributions in the nucleon at low $Q^2$ which incorporate general constraints obtained from the requirements of color coherence of gluon couplings at $x \sim 0$ and the helicity retention properties of perturbative QCD couplings at $x \sim 1.$ The unpolarized predictions are similar to the $D_0'$ distributions given by Martin, Roberts, and Stirling. The predictions for the quark helicity distributions are compared with polarized structure functions measured by the E142 experiment at SLAC and the SMC experiment at CERN., Comment: Correct version of Fig. 1 added, LaTex, 27 pages, plus 4 figures

A new method to perform numerical simulations of light-front Hamiltonians formulated on transverse lattices is introduced. The method is based on a DLCQ formulation for the (continuous) longitudinal directions. The hopping term in the transverse direction introduces couplings between fields defined on neighboring $1+1$-dimensional sheets. Within each sheet, the light-cone imaginary time evolution operator is calculated numerically with high precision using DLCQ. The coupling between neighboring sheets is taken into account using an initial value random walk algorithm based on the ensemble projector Monte Carlo technique and a checkerboard decomposition for the time evolution operator. The structure functions of $\lambda \phi^4$ theory in $2+1$ dimensions are studied as a trial application. The calculations are performed with up to 64 transverse lattice sites. No Tamm-Dancoff truncations are necessary.