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Matching the high momentum modes in a truncated determinant algorithm

Description: Within a truncated determinant algorithm, two alternatives are discussed for including systematically the remaining ultraviolet modes. Evidence is presented that these modes are accurately described by an effective action involving only small Wilson loops.
Date: September 1, 1998
Creator: Duncan, A.; Eichten, E. & Thacker, H., FERMI
Partner: UNT Libraries Government Documents Department

A new scheme for the running coupling constant in gauge theories using Wilson loops

Description: We propose a new renormalization scheme of the running coupling constant in general gauge theories defined by using the Wilson loops. The renormalized coupling constant is obtained from the Cretz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter calculation is performed by adopting the zeta-function resummation techniques. We make a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations.
Date: January 1, 2009
Creator: Kurachi, Masafumi; Bilgici, Erek; Flachi, Antonion; Itou, Etsuko; David Lin, C J; Matsufuru, Hideo et al.
Partner: UNT Libraries Government Documents Department

A lattice formulation of chiral gauge theories

Description: We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative problem.
Date: August 1, 1996
Creator: Bodwin, G.T.
Partner: UNT Libraries Government Documents Department

A lattice formulation of chiral gauge theories

Description: The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.
Date: December 1, 1995
Creator: Bodwin, G.T.
Partner: UNT Libraries Government Documents Department

Factorization and effective action for high-energy scattering in QCD

Description: The author demonstrates that the amplitude of the high-energy scattering can be factorized in a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering.
Date: April 1, 1998
Creator: Balitsky, Ian
Partner: UNT Libraries Government Documents Department

Wilson loops in minimal surfaces

Description: The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.
Date: April 27, 1999
Creator: Drukker, Nadav; Gross, David J. & Ooguri, Hirosi
Partner: UNT Libraries Government Documents Department

Factorization and high-energy effective action

Description: The author demonstrates that the amplitude for high-energy scattering can be factorized as a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering in QCD.
Date: December 1, 1998
Creator: Balitsky, Ian
Partner: UNT Libraries Government Documents Department

Interaction of Wilson loops in the confining vacuum

Description: Nonperturbative and perturbative interaction mechanisms of Wilson loops in gluodynamics are studied within the background field formalism. The first one operates when distance between minimal surfaces of the loops is small and may be important for sea quark effects and strong decay processes. The second mechanism -- perturbative interaction in nonperturbative confining background is found to be physically dominant for all loop configurations characteristic of scattering process. It reduces to perturbative gluon exchanges at small distances, while at larger distances it corresponds to the t-channel exchange of (reggeized) glueball states. Comparison to other approaches is made and possible physical applications are discussed.
Date: April 1, 2002
Creator: Shevchenko, V.I. & Simonov, Yu. A.
Partner: UNT Libraries Government Documents Department

Nonperturbative quark dynamics in baryon

Description: Field-correlator method is used to calculate nonperturbative dynamics of quarks in a baryon. General expression for the 3q Green's function is obtained using Fock-Feynman-Schwinger (world-line) path integral formalism, where all dynamics is contained in the 3q Wilson loop with spin-field insertions. Using lowest cumulant contribution for Wilson loop, one obtains any-shaped string with a deep hole at the string junction position. Using einbein formalism for the quark kinetic terms, one automatically obtains constituent quark masses, calculable through the string tension. Resulting effective action for 3q plus Y-shaped strings is quantized in the path-integral formalism to produce two versions of Hamiltonian, in the c.m., and another in the light-cone system, incorporating confining strings with string junction and quarks with dynamically produced constituent masses. Hyperspherical formalism is used to solve for masses and wave functions. Simple estimates in lowest approximation yield baryon masses in good agreement with experiment without fitting parameters.
Date: April 1, 2002
Creator: Simonov, Yuri A.
Partner: UNT Libraries Government Documents Department

The Two-Loop Six-Point MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory

Description: We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N = 4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.
Date: March 12, 2008
Creator: Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C. et al.
Partner: UNT Libraries Government Documents Department

Quark masses, chiral symmetry, and the U(1) anomaly

Description: The author discusses the mass parameters appearing in the gauge theory of the strong interactions, concentrating on the two flavor case. He shows how the effect of the CP violating parameter {theta} is simply interpreted in terms of the state of the aether via an effective potential for meson fields. For degenerate flavors he shows that a first order phase transition is expected at {theta} = {pi}. The author speculates on the implications of this structure for Wilson`s lattice fermions.
Date: September 17, 1996
Creator: Creutz, M.
Partner: UNT Libraries Government Documents Department

Strange hadronic loops of the proton: A quark model calculation

Description: Nontrivial q{anti q} sea effects have their origin in the low-Q{sup 2} dynamics of strong QCD. The authors present here a quark model calculation of the contribution of s{anti s} pairs arising from a complete set of OZI-allowed strong Y{sup *}K{sup *} hadronic loops to the net spin of the proton, to its charge radius, and to its magnetic moment. The calculation is performed in an ``unquenched quark model'' which has been shown to preserve the spectroscopic successes of the naive quark model and to respect the OZI rule. They speculate that an extension of the calculation to the nonstrange sea will show that most of the ``missing spin'' of the proton is in orbital angular momenta.
Date: October 1, 1996
Creator: Geiger, Paul & Isgur, Nathan
Partner: UNT Libraries Government Documents Department

From the Feynman-Schwinger representation to the non-perturbative relativistic bound state interaction

Description: The authors write the 4-point Green function in QCD in the Feynman-Schwinger representation and show that all the dynamical information are contained in the Wilson loop average. They work out the QED case in order to obtain the usual Bethe-Salpeter kernel. Finally they discuss the QCD case in the non-perturbative regime giving some insight in the nature of the interaction kernel.
Date: March 1, 1997
Creator: Brambilla, N. & Vairo, A.
Partner: UNT Libraries Government Documents Department

Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8

Description: The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U{sub A}(1) symmetry and the {eta}{prime} for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk.
Date: November 1, 1998
Partner: UNT Libraries Government Documents Department

Resummation of threshold corrections in QCD to power accuracy: The Drell-Yan cross section as a case study

Description: Resummation of large infrared logarithms in perturbation theory can, in certain circumstances, enhance the sensitivity to small gluon momenta and introduce spurious nonperturbative contributions. In particular, different procedures--equivalent in perturbation theory--to organize this resummation can differ by 1/Q power corrections. The question arises whether one can formulate resummation procedures that are explicitly consistent with the infrared behavior of finite-order Feynman diagrams. They explain how this problem can be treated and resolved in Drell-Yan (lepton pair) production and briefly discuss more complicated cases, such as top quark production and event shape variables in the e{sup +}e{sup {minus}} annihilation.
Date: May 1, 1996
Creator: Beneke, M. & Braun, V.M.
Partner: UNT Libraries Government Documents Department

Stable superstring relics

Description: The authors investigate the cosmological constraints on exotic stable matter states which arise in realistic free fermionic superstring models. These states appear in the superstring models due to a ``Wilson-line`` breaking of the unifying non-Abelian gauge symmetry. In the models that they consider the unifying SO(10) gauge symmetry is broken at the string level to SO(6) x SO(4), SU(5) x U(1) or SU(3) x SU(2) x U(1). The exotic matter states are classified according to the patterns of the SO(10) symmetry breaking. In SO(6) x XO(4) and SU(5) x U(1) type models one obtains fractionally charged states with Q{sub e.m.} = {+-}1/2. In SU(3) x SU(2) x U(1) type models one also obtains states with the regular charges under the Standard Model gauge group but with ``fractional`` charges under the U(1){sub z{prime}} symmetry. These states include down-like color triplets and electroweak doublets, as well as states which are Standard Model singlets. By analyzing the renormalizable and nonrenormalizable terms of the superpotential in a specific superstring model, the authors show that these exotic states can be stable. They investigate the cosmological constraints on the masses and relic density of the exotic states. They propose that, while the abundance and the masses of the fractionally charged states are highly constrained, the Standard Model-like states, and in particular the Standard Model singlet, are good dark matter candidates.
Date: May 15, 1996
Creator: Chang, S.; Coriano, C. & Faraggi, A.E.
Partner: UNT Libraries Government Documents Department

Perturbative two- and three-loop coefficients from large b Monte Carlo

Description: Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large {beta} on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z{sub 3} tunneling.
Date: October 18, 1999
Creator: Lepage, G.P.; Mackenzie, P.B.; Shakespeare, N.H. & Trottier, H.D.
Partner: UNT Libraries Government Documents Department

Chiral symmetry on the lattice

Description: The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Date: November 1, 1994
Creator: Creutz, M.
Partner: UNT Libraries Government Documents Department

A pot-pourri of results in QCD from large lattice simulations on the CM5

Description: The authors present a status report on simulations being done on 32{sup 3} {times} 64 lattices at {beta} {equals} 6.0 using quenched Wilson fermions. Results for the spectrum, decay constants, the kaon B-parameter B{sub K}, and semi-leptonic form factors are given based on the current statistical sample of 28 configuration. These Grand Challenge calculations are being done on the CM5 at Los Alamos in collaboration with G. Kilcup, S. Sharpe and P. Tamayo. They end with a brief statement of code performance.
Date: December 31, 1993
Creator: Bhattacharya, T. & Gupta, R.
Partner: UNT Libraries Government Documents Department

Bootstrapping the Three-Loop Hexagon

Description: We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.
Date: November 8, 2011
Creator: Dixon, Lance J.; Drummond, James M. & Henn, Johannes M.
Partner: UNT Libraries Government Documents Department

Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

Description: We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Date: February 15, 2012
Creator: Dixon, Lance J.; Drummond, James M. & Henn, Johannes M.
Partner: UNT Libraries Government Documents Department

Wilson fermions at finite temperature

Description: The author conjectures on the phase structure expected for lattice gauge theory with two flavors of Wilson fermions, concentrating on large values of the hopping parameter. Numerous phases are expected, including the conventional confinement and deconfinement phases, as well as an Aoki phase with spontaneous breaking of flavor and parity and a large hopping phase corresponding to negative quark masses.
Date: September 17, 1996
Creator: Creutz, M.
Partner: UNT Libraries Government Documents Department

Cosmological and phenomenological implications of Wilsonian matter in realistic superstring derived models

Description: Superstring phenomenology aims at achieving two goals. The first is to reproduce the observed physics of the Standard Model. The second is to identify experimental signatures of superstring unification which, if observed, will provide further evidence for the validity of superstring theory. I discuss such potential signatures of superstring unification. I propose that proton lifetime constraints imply that the Standard Model gauge group must be obtained directly at the string level. In this case the unifying gauge group, for example SO(10), is broken to the Standard Model gauge group by ``Wilson lines``. The symmetry breaking by ``Wilson line`` has important implications. It gives rise to exotic massless states which cannot fit into multiplets of the original unifying gauge group. This is an important feature because it results in conservation laws which forbid the interaction of the exotic ``Wilsonian`` states with the Standard Model states. The ``Wilsonian`` matter states then have important phenomenological implications. I discuss two such implications: exotic ``Wilsonian`` states as dark matter candidates and ``Wilsonian`` matter as the messenger sector in gauge mediated dynamical SUSY breaking scenarios.
Date: August 1, 1996
Creator: Faraggi, A.E.
Partner: UNT Libraries Government Documents Department