K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory

We calculate results for K to pi and K to 0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low energy constants of the chiral effective theory can be determined. The low energy constants of these matrix elements are necessary for an understanding of the Delta I=1/2 rule, and for calculations of epsilon'/epsilon using current lattice QCD simulations.Comment: 43 pages, 2 figures, uses RevTeX, added and updated reference

Existence and uniqueness for Mean Field Games with state constraints

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption

Dual-species quantum degeneracy of potassium-40 and rubidium-87 on an atom chip

In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time.Comment: 8 pages, 4 figures. To be published in the Proceedings of the 20th International Conference on Atomic Physics, 2006 (Innsbruck, Austria

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.

Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions

In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, the Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a P\'{e}ano like theorem for ordinary differential equations of fractional order.Comment: accepted IJBC, 5 pages, 1 figur

Light hadrons with improved staggered quarks: approaching the continuum limit

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0- meson propagators, and we make a preliminary mass computation for a radially excited 0- meson.Comment: 43 pages, 16 figure

Hyperfine Anomalies in Fr: Boundaries of the Spherical Single Particle Model

We have measured the hyperfine splitting of the 7P(1/2) state at the 100 ppm level in Fr isotopes (Fr-206g,Fr-206m,Fr-207,Fr-209,Fr-213,Fr-221) near the closed neutron shell (N = 126 in Fr-213). The measurements in five isotopes and a nuclear isomeric state of francium, combined with previous determinations of the 7S(1/2) splittings, reveal the spatial distribution of the nuclear magnetization, i.e., the Bohr-Weisskopf effect. We compare our results with a simple shell model consisting of unpaired single valence nucleons orbiting a spherical nucleus, and find good agreement over a range of neutron-deficient isotopes (Fr207-213). Also, we find near-constant proton anomalies for several even-N isotopes. This identifies a set of Fr isotopes whose nuclear structure can be understood well enough for the extraction of weak interaction parameters from parity nonconservation studies

Modeling two-language competition dynamics

During the last decade, much attention has been paid to language competition in the complex systems community, that is, how the fractions of speakers of several competing languages evolve in time. In this paper we review recent advances in this direction and focus on three aspects. First we consider the shift from two-state models to three state models that include the possibility of bilingual individuals. The understanding of the role played by bilingualism is essential in sociolinguistics. In particular, the question addressed is whether bilingualism facilitates the coexistence of languages. Second, we will analyze the effect of social interaction networks and physical barriers. Finally, we will show how to analyze the issue of bilingualism from a game theoretical perspective.Comment: 15 pages, 5 figures; published in the Special Issue of Advances in Complex Systems "Language Dynamics