Vector meson form factors and their quark-mass dependence

The electromagnetic form factors of vector mesons are calculated in an explicitly Poincar\'e covariant formulation, based on the Dyson--Schwinger equations of QCD, that respects electromagnetic current conservation, and unambiguously incorporates effects from vector meson poles in the quark-photon vertex. This method incorporates a 2-parameter effective interaction, where the parameters are constrained by the experimental values of chiral condensate and $f_{\pi}$. This approach has successfully described a large amount of light-quark meson experimental data, e.g. ground state pseudoscalar masses and their electromagnetic form factors; ground state vector meson masses and strong and electroweak decays. Here we apply it to predict the electromagnetic properties of vector mesons. The results for the static properties of the $\rho$-meson are: charge radius $= 0.54 {\rm fm}^2$, magnetic moment $\mu = 2.01$, and quadrupole moment ${\cal Q} = -0.41$. We investigate the quark mass dependence of these static properties and find that our results at the charm quark mass are in agreement with recent lattice simulations. The charge radius decreases with increasing quark mass, but the magnetic moment is almost independent of the quark mass.Comment: 13 pages, 7 figure

Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.Comment: 30 page

Scaling analysis of FLIC fermion actions

The Fat Link Irrelevant Clover (FLIC) fermion action is a variant of the $O(a)$-improved Wilson action where the irrelevant operators are constructed using smeared links. While the use of such smearing allows for the use of highly improved definitions of the field strength tensor $F_{\mu\nu},$ we show that the standard 1-loop clover term with a mean field improved coefficient $c_{\rm sw}$ is sufficient to remove the $O(a)$ errors, avoiding the need for non-perturbative tuning. This result enables efficient dynamical simulations in QCD with the FLIC fermion action.Comment: 5 pages, 3 figure

Pseudoscalar and vector meson form factors from lattice QCD

We present a study of the pseudoscalar and vector meson form factors, calculated using the Fat-Link Irrelevant Clover (FLIC) action in the framework of Quenched Lattice QCD. Of particular interest is the determination of a negative quadrupole moment, indicating that the $\rho$ meson is not spherically symmetric.Comment: 11 pages, 15 figures, 9 table

Light quark electromagnetic structure of baryons

Fascinating aspects of the light quark-mass behavior of baryon electromagnetic form factors are highlighted. Using FLIC fermions on $20^3 \times 40$ quenched ${\cal O}(a^2)$-improved gauge fields, we explore charge radii and magnetic moments at pion masses as light as 300 MeV. Of particular interest is chiral curvature of proton charge radii and magnetic moments, the environmental dependence of strange quark properties in hyperons, and the remarkable signature of quenched chiral-nonanalytic behavior in the magnetic moment of $\Delta$ baryon resonances.Comment: 7 pages, 6 figures, Presented at the 24th International Symposium on Lattice Field Theory (Lattice 2006), Tucson, Arizona, 23-28 Jul 200

Isolating Excited States of the Nucleon in Lattice QCD

We discuss a robust projection method for the extraction of excited-state masses of the nucleon from a matrix of correlation functions. To illustrate the algorithm in practice, we present results for the positive parity excited states of the nucleon in quenched QCD. Using eigenvectors obtained via the variational method, we construct an eigenstate-projected correlation function amenable to standard analysis techniques. The method displays its utility when comparing results from the fit of the projected correlation function with those obtained from the eigenvalues of the variational method. Standard nucleon interpolators are considered, with $2\times 2$ and $3\times 3$ correlation matrix analyses presented using various combinations of source-smeared, sink-smeared and smeared-smeared correlation functions. Using these new robust methods, we observe a systematic dependency of the nucleon excited-state masses on source- and sink-smearing levels. To the best of our knowledge, this is the first clear indication that a correlation matrix of standard nucleon interpolators is insufficient to isolate the eigenstates of QCD.Comment: May 2009.13pp, Minor changes and references adde

Light-Quark FLIC Fermion Simulations of the 1−+1^{-+} Exotic Meson

We investigate the mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields. Access to light quark masses approaching 25 MeV is facilitated by the use of the Fat-Link Irrelevant Clover (FLIC) fermion action, and large ($20^3 \times 40$) lattices. Our results indicate that the $1^{-+}$ exotic exhibits significant curvature close to the chiral limit, and yield a $1^{-+}$ mass in agreement with the $\pi_1 (1600)$ candidate and exclusive of the $\pi_1 (1400)$.Comment: 6 pages, 1 table, 2 figures, talk given at Lattice '05. Removed unccessary figure

Low-lying positive-parity excited states of the nucleon

We present an overview of the correlation-matrix methods developed recently by the CSSM Lattice Collaboration for the isolation of excited states of the nucleon. Of particular interest is the first positive-parity excited-state of the nucleon known as the Roper resonance. Using eigenvectors of the correlation matrix we construct parity and eigenstate projected correlation functions which are analysed using standardized methods. The robust nature of this approach for extracting the eigenstate energies is presented. We report the importance of using a variety of source and sink smearings in achieving this. Ultimately the independence of the eigenstate energies from the interpolator basis is demonstrated. In particular we consider $4\times 4$ correlation matrices built from a variety of interpolators and smearing levels. Using FLIC fermions to access the light quark mass regime, we explore the curvature encountered in the energy of the states as the chiral limit is approached. We report a low-lying Roper state contrasting earlier results using correlation matrices. To the best of our knowledge, this is the first time a low-lying Roper resonance has been found using correlation matrix methods. Finally, we present our results in the context of the Roper results reported by other groups.Comment: 8 pages, 4 figures., Presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin