Chiral Anomaly and Index Theorem on a finite lattice

The condition for a lattice Dirac operator D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is that D possesses exact zero modes satisfying the Atiyah-Singer index theorem. This is also the necessary condition for D to have correct fermion determinant (ratio) which plays the important role of incorporating dynamical fermions in the functional integral.Comment: LATTICE99(chiral fermion), 3 pages, Latex, espcrc2.st

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

Flavor Mixing and the Permutation Symmetry among Generations

In the standard model, the permutation symmetry among the three generations of fundamental fermions is usually regarded to be broken by the Higgs couplings. It is found that the symmetry is restored if we include the mass matrix parameters as physical variables which transform appropriately under the symmetry operation. Known relations between these variables, such as the renormalization group equations, as well as formulas for neutrino oscillations (in vacuum and in matter), are shown to be covariant tensor equations under the permutation symmetry group.Comment: 12 page

Rephasing invariance and neutrino mixing

A rephasing invariant parametrization is introduced for three flavor neutrino mixing. For neutrino propagation in matter, these parameters are shown to obey evolution equations as functions of the induced neutrino mass. These equations are found to preserve (approximately) some characteristic features of the mixing matrix, resulting in solutions which exhibit striking patterns as the induced mass varies. The approximate solutions are compared to numerical integrations and found to be quite accurate.Comment: 18 pages, 6 figure

Renormalization of the Neutrino Mass Matrix

In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.Comment: 15 pages, 1figur

Properties of the Neutrino Mixing Matrix

For neutrino mixing we propose to use the parameter set $X_{i}$ $(=|V_{ei}|^{2})$ and $\Omega_{i}$ $(=\epsilon_{ijk}|V_{\mu j}|^{2}|V_{\tau k}|^{2})$, with two constraints. These parameters are directly measurable since the neutrino oscillation probabilities are quadratic functions of them. Physically, the set $\Omega_{i}$ signifies a quantitative measure of $\mu-\tau$ asymmetry. Available neutrino data indicate that all the $\Omega_{i}$'s are small $(\lesssim O(10^{-1}))$, but with large uncertainties. The behavior of $\Omega_{i}$ as functions of the induced neutrino mass in matter are found to be simple, which should facilitate the analyses of long baseline experiments.Comment: 14 pages, 5 figure

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

A generalized Ginsparg-Wilson relation

We show that, under certain general assumptions, any sensible lattice Dirac operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR). Those assumptions, on the other hand, are mostly dictated by large momentum behaviour considerations. We also show that all the desirable properties often deduced from the standard GWR hold true of the general case as well; hence one has, in fact, more freedom to modify the form of the lattice Dirac operator, without spoiling its nice properties. Our construction, a generalized Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the lattice Dirac operator. We discuss some of these examples, and also present a derivation of the GGWR in terms of a renormalization group transformation with a blocking which is not diagonal in momentum space, but nevertheless commutes with the Dirac operator.Comment: 16 pages, Latex, no figure