We calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size L ≈ 2.5 fm, and a lattice spacing of a ≈ 0.124 fm, for pion masses as light as mπ ≈ 300 MeV, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two-and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the threeflavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU (3) fits are inconsistent with their phenomenological values. Nextto-next-to-leading order SU (2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in mπ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

We present a comprehensive study of the lowest moments of nucleon generalized parton distributions in N f = 2 + 1 lattice QCD using domain wall valence quarks and improved staggered sea quarks. Our investigation includes helicity dependent and independent generalized parton distributions for pion masses as low as 350 MeV and volumes as large as (3.5 fm) 3 , for a lattice spacing of 0.124 fm. We use perturbative renormalization at one-loop level with an improvement based on the non-perturbative renormalization factor for the axial vector current, and only connected diagrams are included in the isosinglet channel.

We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.

The 2D O(3) model with a 9 vacuum term is formulated in terms of Wolff clusters. Each cluster carries an integer or half-integer topological charge. The clusters with charge~1/2 are identified as merons. At 0 =~t he merons are bound in pairs inducing a second order phase transition at which the mass gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the k = 1 Wess-Zumino-Novikov-Witten (WZNW) model. Our results are consistent with Haldane's conjecture fro 1D antiferromagnetic quantum spin chains. PACS numbers: 75.10.Jm Some time ago Haldane conjectured [1] that integer and half-integer 1D antiferromagnetic quantum spin chains behave qualitatively differently. While integer spin chains have a mass gap, half-integer chains should be gapless.This has been confirmed numerically for finite chains of spin 1 and spin 2 [2,3] and analytically for half-integer spins and for spin 1 [4]. The long-range physics of 1D quantum spin chains is described by an effective 2D classical O(3) model. Haldane argued that the effective action for a chain of spins S contains a topological term iOQ Here Q . is the topological charge and 9 = 2n5 is the vacuum angle. Since the physics is periodic in 0, i.e. , 0 E] -~, 7r], integer spins have 0 = 0 and half-integer spins have 0 = vr The st.andard O(3) model at 0 = 0 has a mass gap in agreement with Haldane's conjecture. On the other hand, Haldane's conjecture together with the (nonrigorous) mapping of spin chains on the O(3) model imply that the mass gap disappears at 0 = m. This corresponds to a phase transition in the vacuum angle. Because of the complex action it is notoriously difficult to simulate 0 vacua numerically. A previous numerical study that was limited to~0~( 0. 8m. found no phase transition in that region [5]. In fact, Haldane's conjecture has not yet been verified in the context of the O(3) model. In this paper we use the Wolff cluster algorithm [6] combined with a reweighting technique [7] to attack this problem. The construction of an improved estimator for the topological charge distribution enables us to simulate 0 vacua reliably for any value of 0. Affleck and Haldane have suggested a dynamical mechanism that explains why the mass gap disappears at 0 = vr [3]. In this picture pseudoparticles with topological charge~1/2 -so-called merons -are the relevant degrees of freedom. At 0 = 0 the merons form an ideal gas. They disorder the system and thereby give nonzero mass to the physical particles. At 0 =~, on the other hand, the merons are bound in pairs and thus do not generate mass. Affleck confirmed this picture in a model where the O(3) symmetry is explicitly broken to O(2). Then the merons behave like vortices, and the phase transition in 0 is analogous to the Kosterlitz-Thouless transition of the O(2) model. When the explicit O(3) breaking is switched off, it is unclear if this dynamical picture still holds. In fac...