Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

Hadronic B_c decays as a test of B_c cross section

This paper focuses on disagreement between theoretical predictions and experimental results of the production properties of Bc meson. Hadronic decays of Bc are used to separate predictions of production cross section and predictions of branching ratio. The branching ratios of Bc decays to J/psi + \pi and to J/psi + 3\pi are also presented.Comment: 3 page

Effective models of two-flavor QCD: from small towards large mqm_q

We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD. We consider chiral sector described either using linear sigma model or Nambu-Jona-Lasinio model and study how these models, on the mean-field level when coupled with the Polyakov loop, behave as a function of increasing bare quark (or pion) mass. We find qualitatively similar behaviors for the cases of linear sigma model and Nambu-Jona-Lasinio model and, relating to existing lattice data, show that one cannot conclusively decide which or the two approximate symmetries drives the phase transitions near the physical point

Solutions of the Ginsparg-Wilson Relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13

A note on Zolotarev optimal rational approximation for the overlap Dirac operator

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w (H_w^2)^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2)^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.Comment: 23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev.