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.