315 research outputs found
Four-dimensional lattice chiral gauge theories with anomalous fermion content
In continuum field theory, it has been discussed that chiral gauge theories
with Weyl fermions in anomalous gauge representations (anomalous gauge
theories) can consistently be quantized, provided that some of gauge bosons are
permitted to acquire mass. Such theories in four dimensions are inevitablly
non-renormalizable and must be regarded as a low-energy effective theory with a
finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework
which enables one to study such theories in a non-perturbative level. By
introducing bare mass terms of gauge bosons that impose ``smoothness'' on the
link field, we explicitly construct a consistent fermion integration measure in
a lattice formulation based on the Ginsparg-Wilson (GW) relation. This
framework may be used to determine in a non-perturbative level an upper bound
on the UV cutoff in low-energy effective theories with anomalous fermion
content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar
field, this framework provides also a lattice definition of a non-linear sigma
model with the Wess-Zumino-Witten (WZW) term.Comment: 18 pages, the final version to appear in JHE
A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
We present a gauge-invariant and non-perturbative construction of the
Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac
operator satisfying the Ginsparg-Wilson relation. Our construction covers all
SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable
for a description of the baryon number non-conservation. In infinite volume, it
provides a gauge-invariant regularization of the electroweak theory to all
orders of perturbation theory. First we formulate the reconstruction theorem
which asserts that if there exists a set of local currents satisfying cetain
properties, it is possible to reconstruct the fermion measure which depends
smoothly on the gauge fields and fulfills the fundamental requirements such as
locality, gauge-invariance and lattice symmetries. Then we give a closed
formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE
Domain wall fermion and CP symmetry breaking
We examine the CP properties of chiral gauge theory defined by a formulation
of the domain wall fermion, where the light field variables and
together with Pauli-Villars fields and are utilized. It is shown
that this domain wall representation in the infinite flavor limit is
valid only in the topologically trivial sector, and that the conflict among
lattice chiral symmetry, strict locality and CP symmetry still persists for
finite lattice spacing . The CP transformation generally sends one
representation of lattice chiral gauge theory into another representation of
lattice chiral gauge theory, resulting in the inevitable change of propagators.
A modified form of lattice CP transformation motivated by the domain wall
fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion
invariant, is analyzed in detail; this provides an alternative way to
understand the breaking of CP symmetry at least in the topologically trivial
sector. We note that the conflict with CP symmetry could be regarded as a
topological obstruction. We also discuss the issues related to the definition
of Majorana fermions in connection with the supersymmetric Wess-Zumino model on
the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in
press
Generalized Ginsparg-Wilson algebra and index theorem on the lattice
Recent studies of the topological properties of a general class of lattice
Dirac operators are reported. This is based on a specific algebraic realization
of the Ginsparg-Wilson relation in the form
where stands for a non-negative integer.
The choice corresponds to the commonly discussed Ginsparg-Wilson relation
and thus to the overlap operator. It is shown that local chiral anomaly and the
instanton-related index of all these operators are identical. The locality of
all these Dirac operators for vanishing gauge fields is proved on the basis of
explicit construction, but the locality with dynamical gauge fields has not
been established yet. We suggest that the Wilsonian effective action is
essential to avoid infrared singularities encountered in general perturbative
analyses.Comment: 11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice
Statistics and Mathematical Physics, Tianjin, China, 8-11 October, 2001. To
be published in the Proceedings and in Int. Jour. Mod. Phys.
Neutron electric dipole moment from lattice QCD
We carry out a feasibility study for the lattice QCD calculation of the
neutron electric dipole moment (NEDM) in the presence of the term. We
develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic
form factor at small , in which NEDM is given by where is the momentum transfer and is the
nucleon mass. We first derive a formula which relates , a matrix element
of the electromagnetic current between nucleon states, with vacuum expectation
values of nucleons and/or the current. In the expansion of , the
parity-odd part of the nucleon-current-nucleon three-point function contains
contributions not only from the parity-odd form factors but also from the
parity-even form factors multiplied by the parity-odd part of the nucleon
two-point function, and therefore the latter contribution must be subtracted to
extract . We then perform an explicit lattice calculation employing the
domain-wall quark action with the RG improved gauge action in quenched QCD at
GeV on a lattice. At the quark mass
, corresponding to , we accumulate 730
configurations, which allow us to extract the parity-odd part in both two- and
three-point functions. Employing two different Dirac matrix
projections, we show that a consistent value for cannot be obtained
without the subtraction described above. We obtain 0.024(5) fm for the neutron and
0.021(6) fm for the
proton.Comment: LaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx,
comments added and typos corrected, final version to appear in Phys. Rev.
A Perturbative Study of a General Class of Lattice Dirac Operators
A perturbative study of a general class of lattice Dirac operators is
reported, which is based on an algebraic realization of the Ginsparg-Wilson
relation in the form
where stands for a non-negative integer.
The choice corresponds to the commonly discussed Ginsparg-Wilson relation
and thus to the overlap operator. We study one-loop fermion contributions to
the self-energy of the gauge field, which are related to the fermion
contributions to the one-loop function and to the Weyl anomaly. We
first explicitly demonstrate that the Ward identity is satisfied by the
self-energy tensor. By performing careful analyses, we then obtain the correct
self-energy tensor free of infra-red divergences, as a general consideration of
the Weyl anomaly indicates. This demonstrates that our general operators give
correct chiral and Weyl anomalies. In general, however, the Wilsonian effective
action, which is supposed to be free of infra-red complications, is expected to
be essential in the analyses of our general class of Dirac operators for
dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in
press
Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac
operator does not possess any topological zero modes in
topologically-nontrivial gauge backgrounds, it can reproduce correct axial
anomaly for sufficiently smooth gauge configurations, provided that it is
exponentially-local, doublers-free, and has correct continuum behavior. In this
paper, we calculate the axial anomaly of this lattice Dirac operator in weak
coupling perturbation theory, and show that it recovers the topological charge
density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge
backgroun
Random Matrix Theory and the Spectra of Overlap Fermions
The application of Random Matrix Theory to the Dirac operator of QCD yields
predictions for the probability distributions of the lowest eigenvalues. We
measured Dirac operator spectra using massless overlap fermions in quenched QCD
at topological charge \nu = 0, +- 1 and +- 2, and found agreement with those
predictions - at least for the first non-zero eigenvalue - if the volume
exceeds about (1.2 fm)^4.Comment: 3 pages, talk presented at Lattice2003(chiral
Neutron electric dipole moment with external electric field method in lattice QCD
We discuss a possibility that the Neutron Electric Dipole Moment (NEDM) can
be calculated in lattice QCD simulations in the presence of the CP violating
term. In this paper we measure the energy difference between spin-up
and spin-down states of the neutron in the presence of an uniform and static
external electric field. We first test this method in quenched QCD with the RG
improved gauge action on a lattice at 2 GeV,
employing two different lattice fermion formulations, the domain-wall fermion
and the clover fermion for quarks, at relatively heavy quark mass . We obtain non-zero values of NEDM from calculations with both
fermion formulations. We next consider some systematic uncertainties of our
method for NEDM, using lattice at the same lattice spacing only
with the clover fermion. We finally investigate the quark mass dependence of
NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We
interpret this behavior as a manifestation of the pathology in the quenched
approximation.Comment: LaTeX2e, 51 pages, 43 figures, uses revtex4 and graphicx, References
and comments added, typos corrected, accepted by PR
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