Generalised L\"uroth expansions and a family of Minkowski's Question-Mark functions

The Minkowski's Question-Mark function is a singular homeomorphism of the unit interval that maps the set of quadratic surds into the rationals. This function has deserved the attention of several authors since the beginning of the twentieth century. Using different representations of real numbers by infinite sequences of integers, called $\alpha$-L\"uroth expansions, we obtain different instances of the standard shift map on infinite symbols, all of them topologically conjugated to the Gauss Map. In this note we prove that each of these conjugations share properties with the Minkowski's Question-Mark function: all of them are singular homeomorphisms of the interval, and in the "rational" cases, they map the set of quadratic surds into the set of rational numbers. In this sense, this family is a natural generalisation of the Minkowski's Question-Mark function

Light Light by Julie Joosten

Mathieu Aubin\u27s review of Light Light by Julie Joosten

Staggered Chiral Perturbation Theory

We discuss how to formulate a staggered chiral perturbation theory. This amounts to a generalization of the Lee-Sharpe Lagrangian to include more than one flavor (i.e. multiple staggered fields), which turns out to be nontrivial. One loop corrections to pion and kaon masses and decay constants are computed as examples in three cases: the quenched, partially quenched, and full (unquenched) case. The results for the one loop mass and decay constant corrections have already been presented in Ref. [1].Comment: talk presented by C. Aubin at Lattice2002(spectrum); 3 pages, 1 figur

A new approach for Delta form factors

We discuss a new approach to reducing excited state contributions from two- and three-point correlation functions in lattice simulations. For the purposes of this talk, we focus on the Delta(1232) resonance and discuss how this new method reduces excited state contamination from two-point functions and mention how this will be applied to three-point functions to extract hadronic form factors.Comment: 4 pages, 3 figures, talk given at MENU 2010, Williambsurg, V

Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks

We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu = (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q^2 region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} = (713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering systematic uncertainties not eliminated in this study, we view this as agreement with the current best calculations using the experimental cross section for e^+e^- annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the experimental decay rate of the tau lepton to hadrons, 711.0 (5.0) (0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current lattice calculation.Comment: 44 pages, 4 tables, 17 figures, more discussion on matching the chpt calculation to lattice calculation, typos corrected, refs added, version to appear in PR

Results on improved KS dynamical configurations: spectrum, decay constants, etc

The MILC Collaboration has been producing ensembles of lattice configurations with three dynamical flavors for the past few years. There are now results for three lattice spacings for a variety of light and strange quark masses, ranging down to $m_l=0.1 m_s$, where $m_s$ is the dynamical strange quark mass and $m_l$ is the common mass of the $u$ and $d$ quarks. Recently, the Fermilab, HPQCD, MILC and UKQCD collaborations have presented a summary of results obtained using these lattices. Compared with quenched results, these new calculations show great improvement in agreement with experiment. This talk addresses the technical improvements that make these calculations possible and provides additional details of calculations not presented in the initial summary. We demonstrate that a wide range of hadronic observables can now be calculated to 2--3% accuracy.Comment: 10 pages, 17 figures (16 in color), Lattice2003(plenary), Plenary talk presented at Lattice 2003, Tsukuba, Japan, July 15-19. Also presented at Lattice Hadron Physics workshop, Cairns, Australia, July 22-30, 200