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Geometric Integration Of The Vlasov-Maxwell System With A Variational Particle-in-cell Scheme

Description: A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
Date: March 27, 2012
Creator: Squire, J.; Qin, H. & Tang, W. M.
Partner: UNT Libraries Government Documents Department

Vertex Sensitivity in the Schwinger-Dyson Equations of QCD

Description: The nonperturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the nonperturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a mass-like term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
Date: January 1, 2012
Creator: David J. Wilson, Michael R. Pennington
Partner: UNT Libraries Government Documents Department

Scattering Amplitudes: The Most Perfect Microscopic Structures in the Universe

Description: This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N = 4 super-Yang-Mills theory, as well as (super)gravity. I also provide a pedagogical introduction to some of the basic tools used to organize and illuminate the color and kinematic structure of amplitudes. This article is an invited review introducing a special issue of Journal of Physics A devoted to 'Scattering Amplitudes in Gauge Theories'.
Date: November 4, 2011
Creator: Dixon, Lance J. & /SLAC, /CERN
Partner: UNT Libraries Government Documents Department

Parity Doubling and the S Parameter Below the Conformal Window

Description: We describe a lattice simulation of the masses and decay constants of the lowest-lying vector and axial resonances, and the electroweak S parameter, in an SU(3) gauge theory with N{sub f} = 2 and 6 fermions in the fundamental representation. The spectrum becomes more parity doubled and the S parameter per electroweak doublet decreases when N{sub f} is increased from 2 to 6, motivating study of these trends as N{sub f} is increased further, toward the critical value for transition from confinement to infrared conformality.
Date: October 21, 2011
Creator: Appelquist, T; Babich, R; Brower, R C; Cheng, M; Clark, M A; Cohen, S D et al.
Partner: UNT Libraries Government Documents Department

The $\hbar$ Expansion in Quantum Field Theory

Description: We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Date: October 27, 2010
Creator: Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul & /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
Partner: UNT Libraries Government Documents Department

'Insightful D-branes'

Description: We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon. A key role is played by the dynamics of the scalar fields in the dual gauge theory. This leads to a proposal for a dual description of D-branes falling through the horizon of any AdS black hole. The proposal uses a field-dependent time reparameterization in the field theory. We relate this reparametrization to various gauge invariances of the theory. Finally, we speculate on information loss and the black hole singularity in this context.
Date: August 26, 2010
Creator: Horowitz, Gary; /UC, Santa Barbara; Lawrence, Albion; /Brandeis U. /Santa Barbara, KITP; Silverstein, Eva & /SLAC /Stanford U., Phys. Dept. /Santa Barbara, KITP
Partner: UNT Libraries Government Documents Department

Constructing the S-matrix With Complex Factorization

Description: A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates nontrivial (but familiar) constraints on three-particle coupling constants - these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior {approx} 1/z{sup 2}.
Date: June 19, 2009
Creator: Schuster, Philip C.; /SLAC; Toro, Natalia & /Stanford U., ITP
Partner: UNT Libraries Government Documents Department

Exact Lattice Supersymmetry

Description: We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Date: March 31, 2009
Creator: Catterall, Simon; Kaplan, David B. & Unsal, Mithat
Partner: UNT Libraries Government Documents Department

Planar graphical models which are easy

Description: We describe a rich family of binary variables statistical mechanics models on planar graphs which are equivalent to Gaussian Grassmann Graphical models (free fermions). Calculation of partition function (weighted counting) in the models is easy (of polynomial complexity) as reduced to evaluation of determinants of matrixes linear in the number of variables. In particular, this family of models covers Holographic Algorithms of Valiant and extends on the Gauge Transformations discussed in our previous works.
Date: January 1, 2009
Creator: Chertkov, Michael & Chernyak, Vladimir
Partner: UNT Libraries Government Documents Department

Worldlines as Wilson Lines

Description: Gravitational theories do not admit gauge invariant local operators. We study the limits under which there exists a quasi-local description for a class of non-local gravitational observables where a sum over worldlines plays the role of the Wilson line for gauge theory observables. We study non-local corrections to the local description and circumstances where these corrections become large. We find that these operators are quasi-local in at space and AdS, but fail to be quasi-local in de Sitter space.
Date: April 29, 2008
Creator: Green, Daniel & /SLAC /Stanford U., Dept. Phys.
Partner: UNT Libraries Government Documents Department

Supersymmetry breaking and gauge mediation in models with a generic superpotential

Description: In this note, we present a transparent scheme for finding or creating a (meta)stable vacuum in general supersymmetric models. We derive general conditions for having a supersymmetry breaking vacuum by connecting different models by a coordinate transformation, which is an application of the method used in [16]. In particular, we find that there can be a metastable supersymmetry breaking vacuum in models with the canonical Kahler potential and a generic superpotential. For example, the Wess-Zumino model coupled to the messenger fields possesses a metastable vacuum if coefficients of the superpotential terms satisfy certain inequalities.
Date: January 1, 2008
Creator: Kitano, Ryuichiro & Ookouchi, Yutaka
Partner: UNT Libraries Government Documents Department

First search at CDF for the Higgs boson decaying to a W-boson pair in proton-antiproton collisions at the center-of-mass energy of 1.96 TeV

Description: By way of retaining the gauge invariance of the Standard Model (SM) and giving masses to the W{sup {+-}} and Z{sup 0} bosons and the fermions, the Higgs mechanism predicts the existence of a neutral scalar bosonic particle, whose mass is not exactly known. The Higgs boson is the only experimentally unconfirmed SM particle to date. This thesis documents a search for the Higgs boson in p{bar p} collisions at {radical}s = 1.96 TeV at the Tevatron, using 360 {+-} pb {sup -1} data collected by the Run II Collider Detector at Fermilab (CDF II), as part of the most important quest for contemporary particle physicists. The search was for a Higgs boson decaying to a pair of W{sup {+-}} bosons, where each W boson decays to an electron, a muon or a tau that further decays to an electron or a muon with associated neutrinos. Events with two charged leptons plus large missing energy were selected in data triggered on a high p{sub t} lepton and compared to the signal and backgrounds modeled using Monte Carlo and jet data. No signal-like excess was observed in data. Therefore, upper limits on the HWW production cross-section in the analyzed mass range were extracted using the binned likelihood maximum from distributions of dilepton azimuthal angle at 95% Bayesian credibility level (CL), as shown in the table below.
Date: December 1, 2006
Creator: Chuang, Shan-Huei S.
Partner: UNT Libraries Government Documents Department

GAUGE INVARIANCE IN A Z2 HAMILTONIAN LATTICE GUAGE THEORY.

Description: We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.
Date: July 25, 2005
Creator: SUGIHARA, T.
Partner: UNT Libraries Government Documents Department

Handling the Handbag Diagram in Compton Scattering on the Proton

Description: Poincare invariance, gauge invariance, conservation of parity and time reversal invariance are respected in an impulse approximation evaluation of the handbag diagram. Proton wave functions, previously constrained by comparison with measured form factors, that incorporate the influence of quark transverse and orbital angular momentum (and the corresponding violation of proton helicity conservation) are used. Computed cross sections are found to be in reasonably good agreement with early measurements. The helicity correlation between the incident photon and outgoing proton, K{sub LL}, is both large and positive at back angles. For photon laboratory energies of {le} 6 GeV, we find that K{sub LL} {ne} A{sub LL}, D{sub LL} {ne} 1, and that the polarization P can be large.
Date: February 25, 2004
Creator: Miller, Gerald A.
Partner: UNT Libraries Government Documents Department

THE EARLY DAYS OF LATTICE GAUGE THEORY.

Description: I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles. I wrap up with some challenges for the future.
Date: June 9, 2003
Creator: CREUTZ,M.
Partner: UNT Libraries Government Documents Department

Effective theory approach to unstable particles

Description: The authors present a novel treatment of resonant massive particles appearing as intermediate states in high energy collisions. The approach uses effective field theory methods to treat consistently the instability of the intermediate resonant state. As a result gauge invariance is respected in every step and calculations can in principle be extended to all orders in perturbation theory, the only practical limitation in going to higher orders being the standard difficulties related to multi-loop integrals. The authors believe that the longstanding problem related to the treatment of instability of particles is now solved.
Date: May 19, 2003
Creator: Zanderighi, Giulia
Partner: UNT Libraries Government Documents Department

Gauge invariance in 2Pi effective actions

Description: (Abstract damaged) The 2PI (two particle irreducible) effective action is a general field theoretic tool for addressing this problem. In constructing it one introduces sources for both the fields and their two-point bilinears.
Date: January 1, 2003
Creator: Mottola, E. (Emil)
Partner: UNT Libraries Government Documents Department

Non-Abelian gauge theory on q-Quantum spaces

Description: Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ''vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten map. As an example we consider the Manin plane. Remarks are made concerning the relation between covariant coordinates and covariant derivatives.
Date: August 23, 2002
Creator: Schraml, Stefan L.
Partner: UNT Libraries Government Documents Department

Wilson lines and symmetry breaking on orbifolds

Description: Gauge symmetry breaking by boundary conditions on a manifold is known to be equivalent to Wilson-line breaking through a background gauge field, and is therefore spontaneous. These equivalent pictures are related by a non-periodic gauge transformation. However, we find that boundary condition gauge symmetry breaking on orbifolds is explicit; there is no gauge where all the breaking can be attributed to a background gauge field. In the case of a five-dimensional SU(5) grand unified theory on S{sup 1} = Z{sub 2}, the vacuum with gauge symmetry broken to SU(3) x SU(2) x U(1) and that with SU(5) preserved are completely disconnected: there is no physical process which causes tunneling between the two. This allows a certain localized explicit breaking of SU(5) on one of the orbifold fixed points in the theory with SU(5) breaking. Split multiplets on this fixed point are shown not to induce violations of unitarity in scattering amplitudes.
Date: August 16, 2002
Creator: Hall, Lawrence J.; Murayama, Hitoshi & Nomura, Yasunori
Partner: UNT Libraries Government Documents Department

TRANSITING TOPOLOGICAL SECTORS WITH THE OVERLAP.

Description: The overlap operator provides an elegant definition for the winding number of lattice gauge field configurations. Only for a set of configurations of measure zero is this procedure undefined. Without restrictions on the lattice fields, however, the space of gauge fields is simply connected. I present a simple low dimensional illustration of how the eigenvalues of a truncated overlap operator flow as one travels between different topological sectors.
Date: June 29, 2002
Creator: CREUTZ,M.
Partner: UNT Libraries Government Documents Department

Kinematical twist-3 effects in DVCS as a quark spin rotation

Description: We point out that the kinematical twist-3 contributions to the DVCS amplitude, required to restore electromagnetic gauge invariance of the twist-2 amplitude up to O(t/q{sup 2}), can be understood as a spin rotation applied to the twist-2 quark density matrix in the target. This allows for a compact representation of the twist-3 effects, as well as for a simple physical interpretation.
Date: June 1, 2001
Creator: Radyushkin, A.V. & Weiss, C.
Partner: UNT Libraries Government Documents Department

DVCS amplitude at tree level: Transversality, twist-3, and factorization

Description: We study the virtual Compton amplitude in the generalized Bjorken region (q{sup 2} -> Infinity, t small) in QCD by means of a light-cone expansion of the product of e.m. currents in string operators in coordinate space. Electromagnetic gauge invariance (transversality) is maintained by including in addition to the twist-2 operators 'kinematical' twist-3 operators, which appear as total derivatives of twist-2 operators. The non-forward matrix elements of the elementary twist-2 operators are parametrized in terms of two-variable spectral functions (double distributions), from which twist-2 and 3 skewed distributions are obtained through reduction formulas. Our approach is equivalent to a Wandzura-Wilczek type approximation for the twist-3 skewed distributions. The resulting Compton amplitude is manifestly transverse up to terms of order t/q{sup 2}. We find that in this approximation the tensor amplitude for longitudinal polarization of the virtual photon is finite, while the one for transverse pol arization contains a divergence already at tree level. However, this divergence has zero projection on the polarization vector of the final photon, so that the physical helicity amplitudes are finite.
Date: October 1, 2000
Creator: Radyushkin, A.V. & Weiss, C.
Partner: UNT Libraries Government Documents Department

DVCS amplitude with kinematical twist-3 terms

Description: The authors compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude they include the operators of twist-3 which appear as total derivatives of twist-2 operators. The results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. They find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term.
Date: August 1, 2000
Creator: Radyushkin, A.V. & Weiss, C.
Partner: UNT Libraries Government Documents Department

RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20

Description: This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.
Date: June 1, 2000
Creator: Van Baal, P.; Orland, P. & Pisarski, R.
Partner: UNT Libraries Government Documents Department