1,265 research outputs found

### Chiral Fermions and Anomalies on a Finite Lattice

A recent proposal by Kaplan for a chiral gauge theory on the lattice is
tested with background gauge fields. The spectrum of the finite lattice
Hamiltonian is calculated and the existence of a chiral fermion is
demonstrated. Lattice doublers are found to decouple. The flavor anomalies,
which are in agreement with the continuum anomaly relation, are obeserved on a
finite lattice. Non-trivial anomaly cancellation is observed in a chiral gauge
current.Comment: UCSD/PTH 92-1

### Domain Wall Fermions and Chiral Gauge Theories

We review the status of the domain wall fermion approach to construct chiral
gauge theories on the lattice. In this model an extra, fifth dimension is added
and our 4-dimensional world lives on a domainwall induced by a soliton shaped
mass defect that depends on the extra dimension only. We demonstrate that the
domain wall model gives the correct anomaly structure when external gauge
fields are used. We discuss two ways of adding dynamical gauge fields aiming at
a lattice regularized chiral gauge theory. An approach is presented to keep the
lattice infinite by regarding the fifth direction as the time-axis of a
4-dimensional Hamiltonian. Finally, a prospect to use domain wall fermions for
simulating QCD is given.Comment: 62pages, DESY-94-18

### On the phase structure of a chiral invariant Higgs-Yukawa model

In the past the construction of Higgs-Yukawa models on the lattice was
blocked by the lack of a consistent definition of a chiral invariant Yukawa
coupling term. Here, we consider a chiral invariant Higgs-Yukawa model based on
the overlap operator, realized by the Neuberger-Dirac operator. As a first step
towards a numerical examination of this model we study its phase diagram by
means of an analytic 1/N-expansion, which is possible for small and for large
values of the Yukawa coupling constant. In the case of strong Yukawa couplings
the model effectively becomes an O(4)-symmetric non-linear sigma-model.Comment: 7 pages, 3 figures, Lattice conference 2006, corrected typo

### Zeta-regularized vacuum expectation values

It has recently been shown that vacuum expectation values and Feynman path
integrals can be regularized using Fourier integral operator $\zeta$-function,
yet the physical meaning of these $\zeta$-regularized objects was unknown.
Here we show that $\zeta$-regularized vacuum expectations appear as continuum
limits using a certain discretization scheme. Furthermore, we study the rate of
convergence for the discretization scheme using the example of a
one-dimensional hydrogen atom in $(-\pi,\pi)$ which we evaluate classically,
using the Rigetti Quantum Virtual Machine, and on the Rigetti 8Q quantum chip
"Agave" device. We also provide the free radiation field as an example for the
computation of $\zeta$-regularized vacuum expectation values in a gauge theory.Comment: 36 pages, 2 figures; accepted version (Journal of Mathematical
Physics

### Implementation of Symanzik's Improvement Program for Simulations of Dynamical Wilson Fermions in Lattice QCD

We discuss the implementation of a Sheikholeslami-Wohlert term for
simulations of lattice QCD with dynamical Wilson fermions as required by
Symanzik's improvement program. We show that for the Hybrid Monte Carlo or
Kramers equation algorithm standard even-odd preconditioning can be maintained.
We design tests of the implementation using analytically and numerically
computed cumulant expansions. We find that, for situations where the average
number of Conjugate Gradient iterations exceeds 200, the overhead is only about
20%.Comment: uuencoded gzipped tar-file, Latex2e source file, 6 Figures, 22 pages,
one reference adde

### Study of Liapunov Exponents and the Reversibility of Molecular Dynamics Algorithms

We study the question of lack of reversibility and the chaotic nature of the
equations of motion in numerical simulations of lattice QCD.Comment: latex file with 3 pages, 1 figure. Talk presented at Lattice'96 by C.
Li

### The non-perturbative O(a)-improved action for dynamical Wilson fermions

We compute the improvement coefficient $c_{sw}$ that multiplies the
Sheikholeslami-Wohlert term as a function of the bare gauge coupling for two
flavour QCD. We discuss several aspects concerning simulations with improved
dynamical Wilson fermions.Comment: Latex file, 2 figures, 6 pages, talk given by K.J. at the
International Symposium on Lattice Field Theory, 21-27 July 1997, Edinburgh,
Scotlan

### Chiral Fermions, Anomalies and Chern-Simons Currents on the Lattice

I discuss the zeromode spectrum of lattice chiral fermions in the domain wall
model suggested recently. In particular I give the critical momenta where the
fermions cease to be chiral and show that the spectrum is directly related to
the behaviour of the Chern-Simons current on the lattice. First results for the
domain wall model on the finite lattice indicate that the relevant features of
the model in the infinite system survive for the finite lattice.Comment: (Talk presented at Lattice'92), UCSD/PTH 92-3

### Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

Quasi-PDFs provide a path toward an ab initio calculation of parton
distribution functions (PDFs) using lattice QCD. One of the problems faced in
calculations of quasi-PDFs is the renormalization of a nonlocal operator. By
introducing an auxiliary field, we can replace the nonlocal operator with a
pair of local operators in an extended theory. On the lattice, this is closely
related to the static quark theory. In this approach, we show how to understand
the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a
master formula for renormalizing the nonlocal operator that depends on three
parameters. We present an approach for nonperturbatively determining these
parameters and use perturbation theory to convert to the MS-bar scheme.
Renormalization parameters are obtained for two lattice spacings using Wilson
twisted mass fermions and for different discretizations of the Wilson line in
the nonlocal operator. Using these parameters we show the effect of
renormalization on nucleon matrix elements with pion mass approximately 370
MeV, and compare renormalized results for the two lattice spacings. The
renormalized matrix elements are consistent among the different Wilson line
discretizations and lattice spacings.Comment: 6 pages, 6 figures. v2: added perturbative matching to MS-bar and
additional reference

### Constraining a fourth generation of quarks: non-perturbative Higgs boson mass bounds

We present a non-perturbative determination of the upper and lower Higgs
boson mass bounds with a heavy fourth generation of quarks from numerical
lattice computations in a chirally symmetric Higgs-Yukawa model. We find that
the upper bound only moderately rises with the quark mass while the lower bound
increases significantly, providing additional constraints on the existence of a
straight-forward fourth quark generation. We examine the stability of the lower
bound under the addition of a higher dimensional operator to the scalar field
potential using perturbation theory, demonstrating that it is not significantly
altered for small values of the coupling of this operator. For a Higgs boson
mass of $\sim125\mathrm{GeV}$ we find that the maximum value of the fourth
generation quark mass is $\sim300\mathrm{GeV}$, which is already in conflict
with bounds from direct searches.Comment: 6 pages, 2 figure

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