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The Gribov--Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang--Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, $\sigma_{C}$, to be about three times larger than the Wilson loop string tension, $\sigma_F$. It is far above the Zwanziger variational bound, $\sigma_C \geq \sigma_F$. We argue that the value established in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension's enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as $\sigma_C/\sigma_F = 2.0 \pm 0.4$ and discuss its phenomenological implications., Comment: 13 pages, 6 figures

The Reggeized pion is expected to provide the main contribution to the forward cross section in light meson photoproduction reactions with charge exchange at high energies. We discuss the Reggeization of pion exchange in charged pion photoproduction with an emphasis on consistency with current conservation. We show that the gauge-invariant amplitude for the exchange of a particle with generic even spin $J\geq 2$ in the $t$-channel is analytic at $J=0$, and that it can be interpreted in terms of the nucleon electric current. This enables us to reconcile the dynamics in the $s$- and $u$-channel, which involves also nucleon exchanges, with the amplitude expressed in terms of $t$-channel partial waves, as required by Regge theory., Comment: 16 pages, 4 figures

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials. Agreement is seen with chiral perturbation theory predictions when the chemical potential is small. Comparison to perturbative QCD calculations at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, $\mu_I$, bounds the partition function for a baryon chemical potential $\mu_B=3\mu_I/2$, these calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time., Comment: 17 pages, 14 figures, updated with supplementary material

Forward photoproduction of $\pi^+\pi^-$ pairs with invariant mass of the order of $m_\rho\sim 770$ MeV is traditionally understood to be produced via Pomeron exchange. Based on a detailed analysis of the CLAS photoproduction data, it is shown that the dynamics of two-pion photoproduction for $|t|\gtrsim 0.5$ GeV$^2$ cannot be explained by Pomeron exchange alone. This motivates the development of a new theoretical model of two-pion photoproduction which incorporates both two-pion and pion-nucleon resonant contributions. After fitting free parameters, the model provides an excellent description of the low moments of the angular distribution measured at CLAS, and enables an assessment of the relative contributions of particular production mechanisms and an interpretation of the various features of the data in terms of these mechanisms., Comment: 30 pages, 21 figures

The low-energy finite-volume spectrum of the two-nucleon system at a pion mass of $m_\pi \approx 806$ MeV is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Phys.Rev.D 107 (2023) 9, 094508] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, these results provide compelling evidence for the presence of an additional state in the low-energy spectrum not present in a non-interacting two-nucleon system. Within the space of operators that are considered in this work, the strongest overlap of this state is onto hexaquark operators, and variational analyses based on operator sets containing only dibaryon operators are insensitive to this state over the temporal extent studied here. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated., Comment: 49 pages, 19 Figures

The light-cone distribution amplitude (LCDA) of the pion contains information about the parton momentum carried by the quarks and is an important theoretical input for various predictions of exclusive processes at high energy, including the pion electromagnetic form factor. Progress towards constraining the fourth Mellin moment of the LCDA using the heavy-quark operator product expansion (HOPE) method is presented., Comment: 10 pages, 4 figures, proceedings to talk presented at the 40th International Symposium on Lattice Field Theory, July 31st - August 4th 2023, Fermi National Accelerator Laboratory, Batavia, Illinois, USA. arXiv admin note: text overlap with arXiv:2211.17009

A theoretical model of two-pion photoproduction is presented. The model encodes the prominent $\rho(770)$ resonance and the expected leading background contribution coming from the Deck mechanism. To validate the model, angular moments are computed and compared with the CLAS dataset. After fitting a number of free parameters, the model provides a good description of the data., Comment: 5 pages, 2 figures, proceedings of 17th International Workshop on Meson Physics (MESON2023), June 22nd to 27th, 2023. arXiv admin note: text overlap with arXiv:2310.18990

A calculation of the angular moments of two-pion photoproduction is presented. The underlying theoretical model encodes the prominent $\rho(770)$ resonance and the expected leading background contribution coming from the Deck mechanism. The model contains a number of free parameters which are fit to experimental data. A good description of the angular moments is obtained., Comment: 5 pages, 3 figures. Prepared as proceedings contribution for the 20th International Conference on Hadron Spectroscopy and Structure (HADRON 2023), Genova, Italy, 5-9/6/2023

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of $n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N \times N$ matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 $\pi^+$s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass $m_\pi = 170$ MeV and spacetime volumes of $(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential $\mu_I\sim 1.5 m_\pi$, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq 1/3$) over a wide range of chemical potential before falling towards the asymptotic expectation at $\mu_I\sim 15 m_\pi$. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD., Comment: 16 pages, 18 figures, 1 table

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. This article describes the progress in the lattice QCD calculation of the fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion (HOPE)., Comment: 10 pages, 3 figures, contribution to the proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany

We highlight the need for the development of comprehensive amplitude analysis methods to further our understanding of hadron spectroscopy. Reaction amplitudes constrained by first principles of $S$-matrix theory and by QCD phenomenology are needed to extract robust interpretations of the data from experiments and from lattice calculations., Comment: 15 pages, 9 figures. Contribution to Snowmass 2021

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. In this article, we discuss the calculation of the second and fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion. The resulting value for the second Mellin moment is $ \langle{ \xi^2 }\rangle(\mu = 2~\text{GeV})= 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}$. This result is compatible with those from previous determinations of this quantity., Comment: 17 pages, 8 Figures, 3 Tables; Talk presented at The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology

Parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs) are central non-perturbative objects of interest in high-energy inelastic and elastic scattering, respectively. As a result, an ab-initio determination of these objects is highly desirable. In this paper we present theoretical details for the calculation of the PDFs and LCDAs using a heavy-quark operator product expansion method. This strategy was proposed in a previous paper [Phys. Rev. D 73, 014501 (2006)] for computing higher moments of the PDFs using lattice QCD. Its central feature is the introduction of a fictitious, valence heavy quark. In the current article, we show that the operator product expansion (OPE) of the hadronic matrix element we study can also be expressed as the convolution of a perturbative matching kernel and the corresponding light-cone distribution, which in principle can be inverted to determine the parton momentum fraction dependence. Regarding the extraction of higher moments, this work also provides the one-loop Wilson coefficients in the OPE formulas for the unpolarized PDF, helicity PDF and pseudo-scalar meson LCDAs. Although these Wilson coefficients for the PDFs can be inferred from existing results in the literature, those for the LCDAs are new., Comment: 22 pages, 3 figures; Text updated to be consistent with published version

We explore the feasibility of determining Mellin moments of the pion's light cone distribution amplitude using the heavy quark operator product expansion (HOPE) method. As the first step of a proof of principle study we pursue a determination of the second Mellin moment. We discuss our choice of kinematics which allows us to successfully extract the moment at low pion momentum. We describe the numerical simulation, and describe the data analysis, which leads us to a preliminary determination of the second Mellin moment in the continuum limit in the quenched approximation as $\langle\xi^2\rangle=0.19(7)$ in the $\bar{\text{MS}}$ scheme at 2 GeV., Comment: 9 pages, 8 figures. Contribution to the proceedings of the 2020 Asia-Pacific Symposium on Lattice Field Theory (APLAT 2020). Several citations and additional affiliation added

Current measurements of the high energy behavior of the pion form factor are obtained from pion electroproduction data. These values are model dependent, utilizing the Vanderhaeghen, Guidal and Laget Regge (VGL) Model for their extraction. Recent work which examined the implementation of gauge invariance in that model suggested that it might lead to extracted pion form factors larger than the true values. Here we introduce a new model which preserves the successes of the VGL Model but implements gauge invariance in a new way. To demonstrate the validity of this new approach, we first use it to extract the pion form factor in a simple toy model. When compared with the previous extraction method, the improved model leads to a more reliable extraction. The success in this simple model leads us to reanalyse the electroproduction cross section data, where we obtain comparable values for the pion form factor to those obtained using the VGL procedure., Comment: 7 Pages, 7 Figures, 1 Table

In 2008 the Jefferson Laboratory $F_\pi$ Collaboration released results for the pion electromagnetic form factor, which they extracted from pion electro-production data. The measured values for the pion form factor are model dependent, and require the use of the Vanderhaeghen, Guidal and Laget Regge Model for their extraction. While agreement between this model and data is impressive, the theoretical implementation of gauge invariance is less satisfying. We would like to establish how well the extracted form factor corresponds to the true form factor. To do this, we use a simple toy model, which imposes gauge invariance in a more theoretically satisfying way. The model form factor is extracted from our model cross section using the method employed by the $F_\pi$ Collaboration to extract the experimental pion form factor. We conclude that the reconstructed model form factor is a reasonable representation of the true model form factor for the kinematics chosen, although we note that the extracted form factor is smaller than the true form factor. This suggests that current extracted values of pion form factor may be overestimated., Comment: 13 pages

Corrections motivated by chiral symmetry arguments have long been known to give important contributions to hadronic observables, particularly at low momentum transfer. It is possible to separate these approaches into two broad groups; either the corrections are implemented at the parton level, or at the hadron level. We explore the results of incorporating pion loop corrections at the hadron level to a calculation of electromagnetic form factors in the NJL model. These calculations are compared with the result of an earlier implementation of pion loops at the parton level using the same NJL model formalism. A particular parameter set yields a good description of low energy nucleon properties within both approaches. However, for the $\Sigma^-$ there is a remarkable improvement when the chiral corrections are implemented at the hadronic level., Comment: 7 pages, 4 figures, 4 tables

A neutral scalar meson interacting with a fixed isoscalar nucleon is evolved according to the similarity renormalization group. The fixed source ends up being too singular and an appropriately dressed static source arises from the similarity flow. The fixed source is dressed by a virtual cloud of mesons extending out past the inverse meson mass according to the Yukawa potential. For low energies the source produces a Yukawa mean field which decouples from the remaining meson field fluctuations. The renormalization group procedure for effective particles is also illustrated for this fixed-source model., Comment: 19 pages, PACS numbers: 11.10.Gh, 21.60.-n

We study a simple class of unitary renormalization group transformations governed by a parameter f in the range [0,1]. For f=0, the transformation is one introduced by Wegner in condensed matter physics, and for f=1 it is a simpler transformation that is being used in nuclear theory. The transformation with f=0 diagonalizes the Hamiltonian but in the transformations with f near 1 divergent couplings arise as bound state thresholds emerge. To illustrate and diagnose this behavior, we numerically study Hamiltonian flows in two simple models with bound states: one with asymptotic freedom and a related one with a limit cycle. The f=0 transformation places bound-state eigenvalues on the diagonal at their natural scale, after which the bound states decouple from the dynamics at much smaller momentum scales. At the other extreme, the f=1 transformation tries to move bound-state eigenvalues to the part of the diagonal corresponding to the lowest momentum scales available and inevitably diverges when this scale is taken to zero. We analyze the shift mechanism analytically in a 3x3 matrix model, which displays the essense of this RG behavior., Comment: 27 pages, 3 figures

Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the cutoff to isolate hamiltonians that produce cutoff-independent eigenvalues. The similarity renormalization group is based on similarity transformations that regulate off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form as the cutoff is lowered. This avoids pathologies that plagued tradition transformations acting on hamiltonians, making it possible to produce a well-behaved perturbative approximation of renormalized hamiltonians in asymptotically free theories. We employ a simple two-dimensional delta function example to illustrate this new renormalization technique., Comment: 28 pages, 7 postscript figures

It may be possible to approximate the full pion wave function in light-front QCD using only $q \qbar$ and $q \qbar g$ Fock space components. Removing zero modes and using invariant-mass cutoffs that make a constituent approximation possible leads to non-canonical terms in the QCD hamiltonian, and forces us to work in the broken symmetry phase of QCD in which chiral symmetry breaking operators must appear directly in the hamiltonian because the vacuum is trivial. Assuming any candidate interactions are local in the transverse direction, I argue that they are probably relevant operators so that perturbation theory is not modified at high energies. Since light-front chiral symmetry corresponds to quark helicity conservation, we can readily identify candidate chiral symmetry breaking interactions. The only candidate relevant operator is the quark-gluon emission/absorption operator with a quark spin flip. I argue that this operator can only produce the physical $\pi-\rho$ mass splitting if the $q \qbar g$ component of the pion is significant., Comment: LATEX, 6 pages. To appear in Proceedings of HD 2000, From Hadrons to Strings

We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to force its free-state matrix elements to quickly decrease as the difference of the free masses of the states increases. The cutoff violates a number of physical principles of light-front pure-glue QCD, including Lorentz covariance and gauge covariance. This means that the operators in the Hamiltonian are not required to respect these physical principles. However, by requiring the Hamiltonian to produce cutoff-independent physical quantities and by requiring it to respect the unviolated physical principles of pure-glue QCD, we are able to derive recursion relations that define the Hamiltonian to all orders in perturbation theory in terms of the running coupling. We approximate all physical states as two-gluon states, and use our recursion relations to calculate to second order the part of the Hamiltonian that is required to compute the spectrum. We diagonalize the Hamiltonian using basis-function expansions for the gluons' color, spin, and momentum degrees of freedom. We examine the sensitivity of our results to the cutoff and use them to analyze the nonperturbative scale dependence of the coupling. We investigate the effect of the dynamical rotational symmetry of light-front field theory on the rotational degeneracies of the spectrum and compare the spectrum to recent lattice results. Finally, we examine our wave functions and analyze the various sources of error in our calculation., Comment: 75 pages, 17 figures, 1 table

The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be lowered perturbatively until an infrared cutoff produced by non-perturbative effects such as bound state formation is encountered. We outline the effective field theory and similarity renormalization group techniques for producing renormalized cutoff hamiltonians, and illustrate the control of logarithmic and inverse-power-law errors both techniques provide., Comment: 17 pages, 3 figures, to be published in Proceedings of the 1998 YITP-Workshop on QCD and Hadron Physics, Kyoto, Japan

Light-front quantum chromodynamics may lead to an accurate constituent approximation for the low-energy properties of hadrons. This requires a cutoff that violates explicit gauge invariance and Lorentz covariance, leading to the calculation of a renormalized QCD hamiltonian using a similarity renormalization group. Renormalization repairs broken symmetries, and in light-front field theory it moves dynamical effects that usually require large numbers of partons to few-body effective interactions. This has been shown to work in QED through dominant contributions to the Lamb shift. In QCD logarithmic confinement arises at second order, and initial bound state calculations produce reasonable results., Comment: 26 pages, 5 figures, to be published in Proceedings of the APCTP-RCNP Joint International School on Physics of Hadrons and QCD, Osaka, Japan

Hamiltonian light-front field theory can be used to solve for hadron states in QCD. To this end, a method has been developed for systematic renormalization of Hamiltonian light-front field theories, with the hope of applying the method to QCD. It assumed massless particles, so its immediate application to QCD is limited to gluon states or states where quark masses can be neglected. This paper builds on the previous work by including particle masses non-perturbatively, which is necessary for a full treatment of QCD. We show that several subtle new issues are encountered when including masses non-perturbatively. The method with masses is algebraically and conceptually more difficult; however, we focus on how the methods differ. We demonstrate the method using massive phi^3 theory in 5+1 dimensions, which has important similarities to QCD., Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final published version

We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping any Fock sectors from the theory, and to regulate the Hamiltonian, we suppress the matrix elements of the Hamiltonian between free-particle Fock-space states that differ in free mass by more than a cutoff. The cutoff violates a number of physical principles of the theory, and thus the Hamiltonian is not just the canonical Hamiltonian with masses and couplings redefined by renormalization. Instead, the Hamiltonian must be allowed to contain all operators that are consistent with the unviolated physical principles of the theory. We show that if we require the Hamiltonian to produce cutoff-independent physical quantities and we require it to respect the unviolated physical principles of the theory, then its matrix elements are uniquely determined in terms of the fundamental parameters of the theory. This method is designed to be applied to QCD, but for simplicity, we illustrate our method by computing and analyzing second- and third-order matrix elements of the Hamiltonian in massless phi-cubed theory in six dimensions., Comment: 47 pages, 6 figures; improved referencing, minor presentation changes

Light-front coordinates offer a scenario in which a constituent approximation of hadron structure can emerge from QCD. This requires cutoffs that violate Lorentz covariance and gauge invariance, and a new renormalization group formalism based on a similarity transformation is used with coupling coherence to fix counterterms that restore these symmetries. The counterterms contain functions of longitudinal momentum fractions which severely complicate renormalization, but they also offer possible resolutions of apparent contradictions between the constituent picture and QCD. The similarity transformation and coupling coherence are applied to QED; and it is shown that the resultant Hamiltonian leads to the correct bound state results. The same techniques are applied to QCD and it is shown that a simple confinement mechanism and a reasonable description of heavy quark bound states emerge naturally., Comment: 44 pages, LATEX (including 4 ps-figures), uses epsfig.sty. Based on lectures given at the NATO Advanced Study Institute: Confinement, Duality, and Non-Perturbative Aspects of QCD, Newton Institute, Cambridge, 23 June - 4 July, 1997

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, as revealed by the potential between heavy quarks., Comment: 10 pages, 2 figures (eps files) included. Submitted to Phys. Lett. B

Light-front Hamiltonian methods are being developed to attack bound-state problems in QCD. In this paper we advance the state of the art for these methods by computing the well-known Lamb shift in hydrogen starting from first principles of QED. There are obvious but significant qualitative differences between QED and QCD. In this paper, we discuss the similarities that may survive in a non-perturbative QCD calculation in the context of a precision non-perturbative QED calculation. Central to the discussion are how a constituent picture arises in a gauge field theory, how bound-state energy scales emerge to guide the renormalization procedure, and how rotational invariance emerges in a light-front calculation., Comment: 35 pages, latex, 5 postscript figures included

A constituent parton picture of hadrons with logarithmic confinement naturally arises in weak coupling light-front QCD. Confinement provides a mass gap that allows the constituent picture to emerge. The effective renormalized Hamiltonian is computed to ${\cal O}(g^2)$, and used to study charmonium and bottomonium. Radial and angular excitations can be used to fix the coupling $\alpha$, the quark mass $M$, and the cutoff $\Lambda$. The resultant hyperfine structure is very close to experiment., Comment: 9 pages, 1 latex figure included in the text. Published version (much more reader-friendly); corrected error in self-energy

We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, $\lam$ ($\lam < \Lam$). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, $\lam^2$, is fixed, and the limit, $0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty$, is taken. This upper bound on $\lam^2$ places the effects of low-energy (energy transfer below $\lam$) emission in the effective interactions in the $| e {\overline e} > $ sector. This lower bound on $\lam^2$ insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision., Comment: 46 pages, latex, 3 Postscript figures included, section on remaining corrections added, title changed, error in older version corrected, cutoff placed in a window

It may be possible to derive a constituent approximation for bound states in QCD using hamiltonian light-front field theory. Cutoffs that violate explicit gauge invariance and Lorentz covariance must be employed. A similarity renormalization group and coupling coherence are used to compute the effective hamiltonian as an expansion in powers of the canonical QCD running coupling constant. At second order the QCD hamiltonian contains a confining interaction, which is being studied using bound state perturbation theory. Explicit constituent masses appear because of symmetry violations, and confinement also produces mass gaps, leading to the possibility of an accurate non-perturbative constituent approximation emerging in light-front QCD., Comment: 10 pages, Contribution to the proceedings of Hadron Structure 96, Slovakia, Feb., 1996

Light-front field theory offers a scenario in which a constituent picture of hadrons may arise, but only if cutoffs that violate explicit covariance and gauge invariance are used. The perturbative renormalization group can be used to approximate the cutoff QCD hamiltonian, and even at lowest orders the resultant hamiltonian displays interesting phenomenological features. A general scheme for computing and using these hamiltonians is discussed and it is explicitly shown that a confining interaction appears when the hamiltonian is computed to second order., Comment: 15 pages, latex, no figures. To appear in Proceedings of the workshop `Theory of Hadrons and Light-Front QCD,' Poland, August 1994

Light-front coordinates offer a scenario in which a constituent picture of hadron structure can emerge from QCD, after several difficulties are addressed. Field theoretic difficulties force us to introduce cutoffs that violate Lorentz covariance and gauge invariance, and a new renormalization group formalism based on a similarity transformation is used with coupling coherence to fix cuonterterms that restore these symmetries. The counterterms contain functions of longitudinal momentum fractions that severely complicate renormalization, but they also offer possible resolutions of apparent contradictions between the constituent picture and QCD. The similarity transformation and coupling coherence are applied to QED; and it is shown that the resultant Hamiltonian leads to standard lowest order bound state results, with the Coulomb interaction emerging naturally. The same techniques are applied to QCD and with physically motivated assumptions it is shown that a simple confinement mechanism appears., Comment: corrected version of 1994 lectures, 84 pages, LATEX. Published in "Hadron Physics 94," Proceedings, Gramado, Brazil (World Scientific, 1995)

A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by dropping irrelevant operators and using perturbation theory near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs violate covariance and cluster decomposition, and allow functions of longitudinal momenta to appear in all relevant, marginal, and irrelevant operators. These functions can be determined by insisting that the Hamiltonian display a coupling constant coherence, with the number of couplings that explicitly run with the cutoff scale being limited and all other couplings depending on this scale only through perturbative dependence on the running couplings. Examples are given that show how coupling coherence restores Lorentz covariance and cluster decomposition, as recently speculated by Wilson and the author. The ultimate goal of this work is a practical Lorentz metric version of the renormalization group, and practical renormalization techniques for light-front quantum chromodynamics., Comment: TEX with macros included. 11 figures available upon request. 120 pages. Ohio State preprint OSU-NT-93-117