ηc\eta_c - glueball Mixing and Resonance X(1835)

The mixing of $\eta_c$ and the lowest mass pseudoscalar glueball is estimated within the framework of the instanton liquid model. It is demonstrated that the mixing is large and may explain the difference between the observed mass of the glueball candidate X(1835) and the theoretical prediction of QCD sum rule analysis.Comment: 5 pages, 1 figure, Late

Restricted 132-avoiding permutations

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind.Comment: 10 page

Counting real rational functions with all real critical values

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of this number and pose several related questions.Comment: 12 pages (AMSTEX), 3 picture

QFT results for neutrino oscillations and New Physics

The CP asymmetry in neutrino oscillations, assuming new physics at production and/or detection processes, is analyzed. We compute this CP asymmetry using the standard quantum field theory within a general new physics scenario that may generate new sources of CP and flavor violation. Well known results for the CP asymmetry are reproduced in the case of V -A operators, and additional contributions from new physics operators are derived. We apply this formalism to SUSY extensions of the Standard Model where the contributions from new operators could produce a CP asymmetry observable in the next generation of neutrino experiments.Comment: 6 pages, 3 figures, version to be published in Phys.Rev.

Cluster algebras and Poisson geometry

We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.Comment: minor change