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Articles 1 - 24 of 24
Full-Text Articles in Physics
A Harmonic Solution For Two-Dimensional Adjoint Qcd, Uwe Trittmann
A Harmonic Solution For Two-Dimensional Adjoint Qcd, Uwe Trittmann
Physics Faculty Scholarship
Two-dimensional QCD with adjoint fermions has many attractive features, yet its single-particle content remains largely unknown. To lay the foundation for a crucially improved approximation of the theory’s spectrum, we developed a method to find the basis of eigenstates using the symmetry structure of the asymptotic theory where pair production is disallowed. This method produces complete sets of multidimensional harmonic functions for the massless and the massive theory. Previously only part of such a basis was known. The method presented here should be applicable to other theories and has the promise of factoring out the long-range Coulomb-type part of interactions. …
Higgs Boson Mass In The Standard Model At Two-Loop Order And Beyond, Steve P. Martin, David G. Robertson
Higgs Boson Mass In The Standard Model At Two-Loop Order And Beyond, Steve P. Martin, David G. Robertson
Physics Faculty Scholarship
We calculate the mass of the Higgs boson in the standard model in terms of the underlying Lagrangian parameters at complete 2-loop order with leading 3-loop corrections. A computer program implementing the results is provided. The program also computes and minimizes the standard model effective potential in Landau gauge at 2-loop order with leading 3-loop corrections.
The Bes F0(1810): A New Glueball Candidate, Pedro Bicudo, S.R. Cotanch, Felipe J. Llanes-Estrada, David G. Robertson
The Bes F0(1810): A New Glueball Candidate, Pedro Bicudo, S.R. Cotanch, Felipe J. Llanes-Estrada, David G. Robertson
Physics Faculty Scholarship
We analyze the f0(1810) state recently observed by the BES collaboration via radiative J/ψ decay to a resonant φω spectrum and confront it with DM2 data and glueball theory. The DM2 group only measured ωω decays and reported a pseudoscalar but no scalar resonance in this mass region. A rescattering mechanism from the open flavored KK̄ decay channel is considered to explain why the resonance is only seen in the flavor asymmetric ωφ branch along with a discussion of positive C-parity charmonia decays to strengthen the case for preferred open flavor glueball decays. We also calculate the total decay width …
Tsil: A Program For The Calculation Of Two-Loop Self-Energy Integrals, Steve P. Martin, David G. Robertson
Tsil: A Program For The Calculation Of Two-Loop Self-Energy Integrals, Steve P. Martin, David G. Robertson
Physics Faculty Scholarship
TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge–Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration …
Renormalization Scale Invariant Pqcd Predictions For R(E+ E-) And The Bjorken Sum Rule At Next-To-Leading Order, Michael Binger, Chueng-Ryong Ji, David G. Robertson
Renormalization Scale Invariant Pqcd Predictions For R(E+ E-) And The Bjorken Sum Rule At Next-To-Leading Order, Michael Binger, Chueng-Ryong Ji, David G. Robertson
Physics Faculty Scholarship
We discuss the application of the physical QCD effective charge αV, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the e+e− annihilation ratio Re+e− and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.
On The Bosonic Spectrum Of Qcd (1+1) With Su(N) Currents, Uwe Trittmann
On The Bosonic Spectrum Of Qcd (1+1) With Su(N) Currents, Uwe Trittmann
Physics Faculty Scholarship
In this note we calculate the spectrum of two-dimensional QCD. We formulate the theory with SU(Nc) currents rather than with fermionic operators. We construct the Hamiltonian matrix in DLCQ formulation as a function of the harmonic resolution K and the numbers of flavors N f and colors N c.The resulting numerical eigenvalue spectrum is free from trivial multi-particle states which obscured previous results. The well-known ’t Hooft and large N f spectra are reproduced. In the case of adjoint fermions we present some new results.
Towards Testing The Maldacena Conjecture With Sdlcq, Uwe Trittmann
Towards Testing The Maldacena Conjecture With Sdlcq, Uwe Trittmann
Physics Faculty Scholarship
We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using supersymmetric discrete light-cone quantization (SDLCQ). We present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within 10–15% of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for …
Renormalized Effective Qcd Hamiltonian: Gluonic Sector, David G. Robertson, E.S. Swanson, A.P. Szczepaniak, C.R. Ji, S.R. Cotanch
Renormalized Effective Qcd Hamiltonian: Gluonic Sector, David G. Robertson, E.S. Swanson, A.P. Szczepaniak, C.R. Ji, S.R. Cotanch
Physics Faculty Scholarship
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Głazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Renormalized Effective Hamiltonian Approach To Qcd, David G. Robertson
Renormalized Effective Hamiltonian Approach To Qcd, David G. Robertson
Physics Faculty Scholarship
Continuing our previous QCD Hamiltonian studies in the gluonic and quark sectors, we describe a new renormalization procedure which generates an effective Hamiltonian. The formulation, which is in the Coulomb gauge, provides an improved framework for investigating hadron structure.
Optimal Renormalization Scale And Scheme For Exclusive Processes, Stanley J. Brodsky, Chueng-Ryong Ji, Alex Pang, David G. Robertson
Optimal Renormalization Scale And Scheme For Exclusive Processes, Stanley J. Brodsky, Chueng-Ryong Ji, Alex Pang, David G. Robertson
Physics Faculty Scholarship
We use the Brodsky-Lepage-Mackenzie (BLM) method to fix the renormalization scale of the QCD coupling in exclusive hadronic amplitudes such as the pion form factor and the photon-to-pion transition form factor at large momentum transfer. Renormalization-scheme-independent commensurate scale relations are established which connect the hard scattering subprocess amplitudes that control exclusive processes to other QCD observables such as the heavy quark potential and the electron-positron annihilation cross section. The commensurate scale relation connecting the heavy quark potential, as determined from lattice gauge theory, to the photon-to-pion transition form factor is in excellent agreement with γe⃗ π0e data assuming that the …
Vacuum Structure Of Two-Dimensional Gauge Theories On The Light Front, Gary Mccartor, David G. Robertson, Stephen S. Pinksy
Vacuum Structure Of Two-Dimensional Gauge Theories On The Light Front, Gary Mccartor, David G. Robertson, Stephen S. Pinksy
Physics Faculty Scholarship
We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by reviewing the known light-front solution of the Schwinger model, highlighting the issues that are relevant for reproducing the θ structure of the vacuum. The most important of these are the need to introduce degrees of freedom initialized on two different null planes, the proper incorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regulating singular operator products in a gauge-invariant way. We then consider SU(2) Yang-Mills theory in …
Physical Coupling Schemes And Qcd Exclusive Processes, David G. Robertson
Physical Coupling Schemes And Qcd Exclusive Processes, David G. Robertson
Physics Faculty Scholarship
I discuss application of the BLM method to obtain commensurate scale relations connecting QCD exclusive amplitudes to other observables, in particular the heavy quark potential.
Θ Vacua In The Light-Cone Schwinger Model, Alex C. Kalloniatis, David G. Robertson
Θ Vacua In The Light-Cone Schwinger Model, Alex C. Kalloniatis, David G. Robertson
Physics Faculty Scholarship
We discuss the bosonized Schwinger model in light-cone quantization, using discretization as an infrared regulator. We consider both the light-cone Coulomb gauge, in which all gauge freedom can be removed and a physical Hilbert space employed, and the light-cone Weyl (temporal) gauge, in which the Hilbert space is unphysical and a Gauss law operator is used to select a physical subspace. We describe the different ways in which the θ vacuum is manifested depending on this choice of gauge, and compute the θ-dependence of the chiral condensate in each case.
Light Front Qcd In (1+1)-Dimensions Coupled To Chiral Adjoint Fermions, David G. Robertson, Stephen S. Pinksy
Light Front Qcd In (1+1)-Dimensions Coupled To Chiral Adjoint Fermions, David G. Robertson, Stephen S. Pinksy
Physics Faculty Scholarship
We consider SU(N) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually , which possesses nontrivial topology. In particular, there are N distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization for the case N = 2, using discretization as an infrared regulator. In the discretized form of the theory the nontrivial vacuum structure is associated with the zero momentum mode of the …
The Vacuum In Light Cone Field Theory, David G. Robertson
The Vacuum In Light Cone Field Theory, David G. Robertson
Physics Faculty Scholarship
This is an overview of the problem of the vacuum in light-cone field theory, stressing its close connection to other puzzles regarding light-cone quantization. I explain the sense in which the light-cone vacuum is ``trivial,'' and describe a way of setting up a quantum field theory on null planes so that it is equivalent to the usual equal-time formulation. This construction is quite helpful in resolving the puzzling aspects of the light-cone formalism. It furthermore allows the extraction of effective Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space in which the vacuum state is simple. The …
Light Cone Quantization And Qcd Phenomenology, Stanley J. Brodsky, David G. Robertson
Light Cone Quantization And Qcd Phenomenology, Stanley J. Brodsky, David G. Robertson
Physics Faculty Scholarship
In principle, quantum chromodynamics provides a fundamental description of hadronic and nuclear structure and dynamics in terms of their elementary quark and gluon degrees of freedom. In practice, the direct application of QCD to reactions involving the structure of hadrons is complex because of the interplay of nonperturbative effects such as color confinement and multi-quark coherence. A crucial tool in analyzing such phenomena is the use of relativistic light-cone quantum mechanics and Fock state methods to provide tractable and consistent treatments of relativistic many-body systems. We begin with a brief introduction to light-cone field theory, stressing how it may allow …
The Mandelstam-Leibbrandt Prescription In Light Cone Quantization Gauge Theories, Gary Mccartor, David G. Robertson
The Mandelstam-Leibbrandt Prescription In Light Cone Quantization Gauge Theories, Gary Mccartor, David G. Robertson
Physics Faculty Scholarship
Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.
On The Discretized Light Cone Quantization Of Electrodynamics, Alex C. Kalloniatis, David G. Robertson
On The Discretized Light Cone Quantization Of Electrodynamics, Alex C. Kalloniatis, David G. Robertson
Physics Faculty Scholarship
Discretized light-cone quantization of (3+1)-dimensional electrodynamics is discussed, with careful attention paid to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed, and the corresponding relations that determine the zero modes of the gauge field are obtained. One particularly natural gauge choice in the zero mode sector is identified, for which the constraint relations are simplest and the fields may be taken to satisfy the usual canonical commutation relations. The constraints are solved in perturbation theory, and the Poincaré generators Pμ are constructed. The effect of …
Light Front Qcd And The Constituent Quark Model, Kenneth G. Wilson, David G. Robertson
Light Front Qcd And The Constituent Quark Model, Kenneth G. Wilson, David G. Robertson
Physics Faculty Scholarship
A general strategy is described for deriving a constituent approximation to QCD, inspired by the constituent quark model and based on light-front quantization. Some technical aspects of the approach are discussed, including a mechanism for obtaining a confining potential and ways in which spontaneous chiral symmetry breaking can be manifested
Light Cone Quantization Of Electrodynamics, David G. Robertson
Light Cone Quantization Of Electrodynamics, David G. Robertson
Physics Faculty Scholarship
Light-cone quantization of (3+1)-dimensional electrodynamics is discussed, using discretization as an infrared regulator and paying careful attention to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed and the corresponding relations that determine the constrained modes of the gauge field are obtained. The constraints are solved perturbatively and the structure of the theory is studied to lowest nontrivial order.
Light Cone Quantization Of Gauge Fields, Gary Mccartor, David G. Robertson
Light Cone Quantization Of Gauge Fields, Gary Mccartor, David G. Robertson
Physics Faculty Scholarship
Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the “discretized” light-cone quantization of gauge fields are discussed.
On Spontaneous Symmetry Breaking In Discretized Light Cone Field Theory, David G. Robertson
On Spontaneous Symmetry Breaking In Discretized Light Cone Field Theory, David G. Robertson
Physics Faculty Scholarship
The problem of spontaneous symmetry breaking in scalar field theories quantized on the light cone is considered. Within the framework of "discretized" light-cone field theory, a constrained zero mode of the scalar field, which is necessary for obtaining a consistent dynamics, is responsible for supporting nonzero vacuum expectation values classically. This basic structure is shown to carry over to the quantum theory as well, and the consistency of the formalism is checked in an explicit perturbative calculation in (1+1)-dimensional φ4 theory.
Composite Operator Renormalization And The Trace Anomaly, David G. Robertson
Composite Operator Renormalization And The Trace Anomaly, David G. Robertson
Physics Faculty Scholarship
The general connection between the renormalization of elementary fields and couplings and of appropriate composite operators is discussed. A general method is presented for computing the anomalous dimension matrix of the lagrangian composite operators, to all orders in perturbation theory, in terms of the elementary beta functions and anomalous dimensions. The trace anomaly for a general field theory is determined.
Anomalous Dimensions Of Anisotropic Gauge Theory Operators, David G. Robertson, Frank Wilczek
Anomalous Dimensions Of Anisotropic Gauge Theory Operators, David G. Robertson, Frank Wilczek
Physics Faculty Scholarship
The anomalous dimensions of the anisotropic dimension four operators in SU(N) gauge theory coupled to fermions are calculated to lowest order. The possibility of comparison with numerical simulations is pointed out.