93,344 research outputs found

### A note on the solutions of the Ginsparg-Wilson relation

The role of R in the solutions of the Ginsparg-Wilson relation is discussed.Comment: LaTeX, 12 pages, 4 figures, Equation (11) has been symmetrized to
satisfy the hermiticity conditio

### A construction of chiral fermion action

According to the necessary requirements for a chirally symmetric Dirac
operator, we present a systematic construction of such operators. We formulate
a criterion for the hermitian operator which enters the construction such that
the doubled modes are decoupled even at finite lattice spacing.Comment: 6 page

### The Index and Axial Anomaly of a lattice Dirac operator

A remarkable feature of a lattice Dirac operator is discussed. Unlike the
Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson
lattice Dirac operator does not possess topological zero modes for any
topologically-nontrivial background gauge fields, even though it is
exponentially-local, doublers-free, and reproduces correct axial anomaly for
topologically-trivial gauge configurations.Comment: 3 pages, LaTex, Lattice2001(chiral

### The Index of a Ginsparg-Wilson Dirac operator

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed.
Unlike the Dirac operator for massless fermions in the continuum, this lattice
Dirac operator does not possess topological zero modes for any
topologically-nontrivial background gauge fields, even though it is
exponentially-local, doublers-free, and reproduces correct axial anomaly for
topologically-trivial gauge configurations.Comment: 8 pages, minor changes, the version to appear in Phys. Lett.

### Quenched chiral logarithms in lattice QCD with overlap Dirac quarks

We examine quenched chiral logarithms in lattice QCD with overlap Dirac
quarks. From our data of m_pi^2, we determine the coefficient of quenched
chiral logarithm delta = 0.203(14), 0.176(17), 0.193(17) and 0.200(13) for
lattices of sizes 8^3 times 24, 10^3 times 24, 12^3 times 24 and 16^3 times 32
respectively. Also, for the first three lattice sizes, we measure the index
susceptibility of the overlap Dirac operator, and use the exact relation
between the index susceptibility and the eta' mass in quenched chiral
perturbation theory to obtain an independent determination of delta =
0.198(27), 0.173(24), 0.169(22), which are in good agreement with those
determined from m_pi^2.Comment: Lattice2002(chiral), 3 pages, 2 figure

### A computational system for lattice QCD with overlap Dirac quarks

We outline the essential features of a Linux PC cluster which is now being
developed at National Taiwan University, and discuss how to optimize its
hardware and software for lattice QCD with overlap Dirac quarks. At present,
the cluster constitutes of 30 nodes, with each node consisting of one Pentium 4
processor (1.6/2.0 GHz), one Gbyte of PC800 RDRAM, one 40/80 Gbyte hard disk,
and a network card. The speed of this system is estimated to be 30 Gflops, and
its price/performance ratio is better than $1.0/Mflops for 64-bit (double
precision) computations in quenched lattice QCD with overlap Dirac quarks.Comment: 3 pages, Lattice 2002(machine

### X(3872) in lattice QCD with exact chiral symmetry

We investigate the mass spectrum of $1^{++}$ exotic mesons with quark
content (\c\q\cbar\qbar) , using molecular and diquark-antidiquark
operators, in quenched lattice QCD with exact chiral symmetry. For the
molecular operator \{(\qbar\gamma_i\c)(\cbar\gamma_5\q)-
(\cbar\gamma_i\q)(\qbar\gamma_5\c) \} and the diquark-antidiquark operator
\{(\q^T C \gi \c)(\qbar C \gamma_5 \cbar^T)-(\qbar C \gi^T \cbar^T)(\q^T C
\gamma_5 \c) \} , both detect a resonance with mass around $3890 \pm 30$ MeV
in the limit $m_q \to m_u$, which is naturally identified with $X(3872)$.
Further, heavier exotic meson resonance with $J^{PC} = 1^{++}$ is also
detected, with quark content (\c\s\cbar\sbar) around $4100 \pm 50$ MeV.Comment: 11 pages, 6 figures, v2: eq.(6) has been corrected, 4-charm operators
are omitted, and references are update

### Baryon Masses in Lattice QCD with Exact Chiral Symmetry

We investigate the baryon mass spectrum in quenched lattice QCD with exact
chiral symmetry. For 100 gauge configurations generated with Wilson gauge
action at $\beta = 6.1$ on the $20^3 \times 40$ lattice, we compute
(point-to-point) quark propagators for 30 quark masses in the range $67 {MeV}
\le m_q \le 1790 {MeV}$. For baryons only composed of strange and charm
quarks, their masses are extracted directly from the time correlation
functions, while for those containing $u (d)$ light quarks, their masses are
obtained by chiral extrapolation to $m_\pi = 135$ MeV. Our results of baryon
masses are in good agreement with experimental values, except for the negative
parity states of $\Lambda$ and $\Lambda_c$. Further, our results of charmed
(including doubly-charmed and triply-charmed) baryons can serve as predictions
of QCD.Comment: 4 pages, 2 EPS figures, to appear in the Proceedings of Baryons 2004,
Palaiseau, France, October 25-29, 200

### Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$
with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is
constructed. It is shown that this sequence of topologically-proper lattice
Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This
suggests that the locality of a lattice Dirac operator is irrelevant to its
index.Comment: 4 pages, 1 EPS figure, talk presented at Lattice'00 (Chiral Fermion

### Some remarks on the Ginsparg-Wilson fermion

We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson
relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original
Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An
explicit realization of D follows from the Overlap construction. The general
properties of D are derived. The chiral properties of these higher-order (k >
0) realizations of Overlap Dirac operator are compared to those of the
Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial
anomaly and the fermion determinant in a background gauge field. Our present
results (up to lattice size 16 x 16) indicate that the chiral properties of the
Neuberger-Dirac operator are better than those of higher-order ones.Comment: 20 pages, minor changes in v3, to appear in Nucl. Phys.

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