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S. Dalley

Publications and source records attributed to S. Dalley.

At least 19 recordsLinked to original sources
arXiv2013

Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties.

hep-ph↗
arXiv2005

SU(N_c -> infinity) Lattice Data and Degrees of Freedom of the QCD string

Lattice simulation data on the critical temperature and long-distance potential, that probe the degrees of freedom of the QCD string, are critically reviewed. It is emphasized that comparison of experimental or SU(N_c) lattice data, at finite number of colors N_c, with free string theory can be misleading due to string interactions. Large-N_c extrapolation of pure lattice gauge theory data, in both 3 and 4 dimensions, indicates that there are more worldsheet degrees of freedom than the purely massless transverse ones of the free Nambu-Goto string. The extra variables are consistent with massive modes of oscillation that effectively contribute like c ~ 1/2 conformal degrees of freedom to highly excited states. As a concrete example, the highly excited spectrum of the Chodos-Thorn relativistic string in 1+1 dimensions is analyzed, where there are no transverse oscillations. It is found that the asymptotic density of states for this model is characteristic of a c=1/2 conformal worldsheet theory. The observations made here should also constrain the backgrounds of holographic string models for QCD.

hep-th↗
arXiv2005

Finite Temperature Gauge Theory from the Transverse Lattice

Numerical computations are performed and analytic bounds are obtained on the excited spectrum of glueballs in SU(infinity) gauge theory, by transverse lattice Hamiltonian methods. We find an exponential growth of the density of states, implying a finite critical (Hagedorn) temperature. It is argued that the Nambu-Goto string model lies in a different universality class.

hep-ph↗
arXiv2005

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU(N) gauge theory with massless quarks if that theory has a condensate of fermion lightcone zero modes. The symmetry breaking appears as induced interactions in an effective lightcone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1+1-dimensional reduced models of gauge theory.

hep-ph↗
arXiv2004

Small-x Behaviour of Lightcone Wavefunctions in Transverse Lattice Gauge Theory

We study the behaviour of lightcone wavefunctions, in coarse transverse lattice gauge theory, when one or more parton lightcone momenta are small. This probes the limit of hadron structure at large and small Bjorken x. Finite-energy boundary conditions on boundstates allow one to derive the analytic form of wavefunctions in this region. This leads to simple, universal predictions for the behaviour of quark generalised parton distributions near their endpoints. For the first few meson wavefunctions at large N_c, we give the simplest ansatz that incorporates all the boundary conditions.

hep-ph↗
arXiv2004

Generalised Parton Distributions of the Pion on the Transverse Lattice

The quark generalised parton distributions of the pion are calculated from lightcone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite boundstate lightcone energy conditions, is given for the lightcone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.

hep-ph↗
arXiv2003

Recent Results on the Transverse Lattice

We review recent progress of field theory on a transverse lattice including: realistic calculations of pion structure in large-N_c QCD; fermion doubling and chiral symmetry; a new strong coupling limit; supersymmetry on the transverse lattice; lightcone zero-mode analysis.

hep-ph↗
arXiv2002

Transverse lattice calculation of the pion light-cone wavefunctions

We calculate the light-cone wavefunctions of the pion by solving the meson boundstate problem in a coarse transverse lattice gauge theory using DLCQ. A large-N_c approximation is made and the light-cone Hamiltonian expanded in massive dynamical fields at fixed lattice spacing. In contrast to earlier calculations, we include contributions from states containing many gluonic link-fields between the quarks.The Hamiltonian is renormalised by a combination of covariance conditions on boundstates and fitting the physical masses M_rho and M_pi, decay constant f_pi, and the string tension sigma. Good covariance is obtained for the lightest 0^{-+} state, which we identify with the pion. Many observables can be deduced from its light-cone wavefunctions.After perturbative evolution,the quark valence structure function is found to be consistent with the experimental structure function deduced from Drell-Yan pi-nucleon data in the valence region x > 0.5. In addition, the pion distribution amplitude is consistent with the experimental distribution deduced from the pi gamma^* gamma transition form factor and diffractive dissociation. A new observable we calculate is the probability for quark helicity correlation. We find a 45% probability that the valence-quark helicities are aligned in the pion.

hep-ph↗
arXiv2001

Mesons on a transverse lattice

The meson eigenstates of the light-cone Hamiltonian in a coarse transverse lattice gauge theory are investigated. Building upon previous work in pure gauge theory, the Hamiltonian and its Fock space are expanded in powers of dynamical fields. In the leading approximation, the couplings appearing in the Hamiltonian are renormalised by demanding restoration of space-time symmetries broken by the cut-off. Additional requirements from chiral symmetry are discussed and difficulties in imposing them from first principles in the leading approximation are noted. A phenomenological calculation is then performed, in which chiral symmetry in spontaneously broken form is modelled by imposing the physical pion-rho mass splitting as a constraint. The light-cone wavefunctions of the resulting Hamiltonian are used to compute decay constants, form factors and quark momentum and spin distributions for the pion and rho mesons. Extensions beyond leading order, and the implications for first principles calculations, are briefly discussed.

hep-ph↗
arXiv2000

Precision study of large-N Yang-Mills theory in 2+1 dimensions

The boundstate problem in 2+1-dimensional large-N Yang-Mills theory is accurately solved using the light-front Hamiltonian of transverse lattice gauge theory. We conduct a thorough investigation of the space of couplings on coarse lattices, finding a single renormalised trajectory on which Poincaré symmetries are enhanced in boundstate solutions. Augmented by existing data from finite-N Euclidean lattice simulations, we obtain accurate estimates of the low-lying glueball spectrum at N=infinty

hep-lat↗
arXiv2000

Transverse Lattice

The transverse lattice approach to non-perturbative light-front hamiltonian QCD is described. Preliminary results on the pi-rho system are presented, at fixed DLCQ and Tamm-Dancoff cut-offs. A renormalised, approximately Lorentz covariant light-front hamiltonian is found to leading order of the colour-dielectric expansion, compatible with a massless pion. The pi light-front wavefunction is compared with experiment. Exclusive processes agree reasonably well, given the approximations, but inclusive processes, sensitive to higher Fock state structure, still exhibit large cut-off artifacts.

hep-ph↗
arXiv1999

Introduction to transverse lattice gauge theory

I review a new treatment of an old idea for light-front quantization of lattice gauge theories and give new results from some illustrative calculations: [I] transverse lattice gauge theory; [II] pure glue; [III] heavy sources and winding modes; [IV] an example -- large-N QCD in 2+1 dimensions.

hep-lat↗
arXiv1999

Glueballs on a transverse lattice

Accurate non-perturbative calculations of glueballs are performed using light-front quantised SU(N) gauge theory, to leading order of the 1/N expansion. Based on early work of Bardeen and Pearson, disordered gauge-covariant link variables M on a coarse transverse lattice are used to approximate the physical gauge degrees of freedom. Simple energetics imply that, at lattice spacings of order the inverse QCD scale, the effective light-front Hamiltonian can be expanded in gauge-invariant powers of M: a colour-dielectric expansion. This leads to a self-consistent constituent structure of boundstates. We fix the couplings of this expansion by optimising Lorentz covariance of low-energy eigenfunctions. To lowest non-trivial order of the expansion, we have found a one-parameter trajectory of couplings that enhances Lorentz covariance. On this trajectory the masses of nearly-covariant glueball states exhibit approximate scaling, having values consistent with large-N extrapolations of continuum results from other methods. There is very little variation with N in pure Yang-Mills theory: the lightest glueball mass changes by only a few percent between SU(3) and SU(infinity). The corresponding light-front wavefunctions show an unconventional structure. We also examine restoration of rotational invariance in the heavy-source potential.

hep-lat↗
arXiv1999

Glueball calculations in large-N_c gauge theory

We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wavefunctions in the leading order of the 1/N_c colour expansion. We find 0^{++}, 2^{++}, and 1^{+-} glueballs having masses consistent with N_c=3 data available from Euclidean lattice path integral methods. The wavefunctions exhibit a light-front constituent gluon structure.

hep-th↗
arXiv1998

Colour-Dielectric Gauge Theory on a Transverse Lattice

We investigate in some detail consequences of the effective colour-dielectric formulation of lattice gauge theory using the light-cone Hamiltonian formalism with a transverse lattice. As a quantitative test of this approach, we have performed extensive analytic and numerical calculations for 2+1-dimensional pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one effectively studies a 1+1-dimensional gauge theory coupled to matter in the adjoint representation. We study the structure of coupling constant space for our effective potential by comparing with the physical results available from conventional Euclidean lattice Monte Carlo simulations of this system. In particular, we calculate and measure the scaling behaviour of the entire low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic density of states, and deconfining temperature. We employ a new hybrid DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian matrix elements, along with extrapolation in Tamm-Dancoff truncation, significantly reducing numerical errors. Finally we discuss, in light of our results, what further measurements and calculations could be made in order to systematically remove lattice spacing dependence from our effective potential a priori.

hep-ph↗
arXiv1998

Transverse Lattice Approach to Light-Front Hamiltonian QCD

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the potential between heavy sources and the structure of the glueballs from their light-front wavefunctions. Finally, we briefly discuss the extension of these calculations to 3+1-dimensions.

hep-th↗