Finite Volume Effects and Quenched Chiral Logarithms

We have measured the valence pion mass and the valence chiral condensate on lattice configurations generated with and without dynamical fermions. We find that our data and that of others is well represented by a linear relationship between $m_{\pi}^2$ and the valence quark mass, with a non-zero intercept. For our data, we relate the intercept to finite volume effects visible in the valence chiral condensate. We see no evidence for the singular behavior expected from quenched chiral logarithms.Comment: 5 pages, Latex with included macro. 4 encapsulated postscript figures included. Contribution to Lattice '9

Risk and Utility in Portfolio Optimization

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present here a modification of MPT based on the inclusion of separate risk and utility criteria. We define risk as the probability of failure to meet a pre-established investment goal. We define utility as the expectation of a utility function with positive and decreasing marginal value as a function of yield. The emphasis throughout is on long investment horizons for which risk-free assets do not exist. Analytic results are presented for a Gaussian probability distribution. Risk-utility relations are explored via empirical stock-price data, and an illustrative portfolio is optimized using the empirical data.Comment: 10 pages, 1 figure, presented at 2002 Conference on Econophysics in Bali Indonesi

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.Comment: 26 pages, 2 figures (using psfig). Version to appear in PRD (clarifications added to introduction and section 6; typos corrected; references updated

K→ππK \to \pi \pi Decays with Domain Wall Fermions: Towards Physical Results

We are using domain wall fermions to study $K \to \pi \pi$ matrix elements by measuring $K \to \pi$ and $K \to 0$ matrix elements on the lattice and employing chiral perturbation theory to relate these to the desired physical result. The residual chiral symmetry breaking of domain wall fermions with a finite extent in the fifth dimension impacts these measurements. Using the Ward-Takahashi identities, we investigate residual chiral symmetry breaking effects for divergent quantities and study pathologies of the quenched approximation for small quark mass. We then discuss the $\Delta S = 1$ operator $O_2$, where chiral symmetry is vital for the subtraction of unphysical effects.Comment: 4 pages, 3 figures, Lattice 2000 (Hadronic Matrix Elements), RBC Collaboration, corrected equations 2 and

Hadronic Electromagnetic Properties at Finite Lattice Spacing

Electromagnetic properties of the octet mesons as well as the octet and decuplet baryons are augmented in quenched and partially quenched chiral perturbation theory to include O(a) corrections due to lattice discretization. We present the results for the SU(3) flavor group in the isospin limit as well as the results for SU(2) flavor with non-degenerate quarks. These corrections will be useful for extrapolation of lattice calculations using Wilson valence and sea quarks, as well as calculations using Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 19 pages, 0 figures, RevTeX