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.

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

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

Electroweak radiative corrections and unitarity of Standard Model

Electroweak corrections to longitudinal gauge and Higgs boson scattering amplitudes are calculated. Due to Sudakov double logarithms, the effect is a suppression of amplitude that grows rapidly with increasing center of mass energy leading to significant reduction of cross sections compared to tree level results. For example, the suppression factor for the cross section of $W^+_{\text{L}}W^-_{\text{L}}$ scattering due to these corrections varies from 0.3 at the center of mass energy of $100\text{TeV}$ to a factor of $10^{-12}$ at the center of mass energy of $10^{13}\text{TeV}$. The modification of SM unitarity bound due to these corrections is obtained.Comment: 9 pages, 5 figures, information on v2: some minor typos fixed, published versio

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

Probing the Low-x Structure of the Nucleus with the PHENIX Detector

One of the fundamental goals of the PHENIX experiment is to understand the structure of cold nuclear matter, since this serves as the initial state for heavy-ion collisions. Knowing the initial state is vital for interpreting measurements from heavy-ion collisions. Moreover, the structure of the cold nucleus by itself is interesting since it is a test-bed for our understanding of QCD. In particular there is the possibility of novel QCD effects such as gluon saturation at low-x in the nucleus. At RHIC we can probe the behavior of gluons at low-x by measuring the pair cross-section of di-hadrons from di-jets in d+Au collisions. Our results show a systematic decrease in the pair cross-section as one goes to smaller impact parameters of the nucleus, and also as one goes to lower Bjorken x. There is a possibility that these interesting effects come from gluon recombination at low x in the Au nucleus.Comment: 4 pages, 3 figures, to be published in the Proceedings of the XX International Workshop on Deep Inelastic Scattering, University of Bonn, 26-30th March 201