Quark Contributions to Nucleon Momentum and Spin from Domain Wall fermion calculations

We report contributions to the nucleon spin and momentum from light quarks calculated using dynamical domain wall fermions with pion masses down to 300 MeV and fine lattice spacing a=0.084 fm. Albeit without disconnected diagrams, we observe that spin and orbital angular momenta of both u and d quarks are opposite, almost canceling in the case of the d quark, which agrees with previous calculations using a mixed quark action. We also present the full momentum dependence of n=2 generalized form factors showing little variation with the pion mass.Comment: 7 pages, 5 figures, NT-LBNL-11-020, MIT-CTP-4323. Presented at the 29th International Symposium on Lattice Field Theory (Lattice 2011), Squaw Valley, California, 10-16 Jul 201

Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter

Each of the local isometry groups arising in 3d gravity can be viewed as the group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement, and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for Euclidean signature with positive cosmological constant, the local isometry groups are equipped with the Poisson-Lie structure of a classical double. We calculate the dressing action of the factor groups on each other and find, amongst others, a simple and unified description of the symplectic leaves of SU(2) and SL(2,R). We also compute the Poisson structure on the dual Poisson-Lie groups of the local isometry groups and on their Heisenberg doubles; together, they determine the Poisson structure of the phase space of 3d gravity in the so-called combinatorial description.Comment: 34 pages, minor corrections, references adde

A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions

We define and discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on the topology of spacetime there are typically finitely many topological degrees of freedom as well as topological interactions of Aharonov-Bohm type between massive objects. In order to capture these topological aspects we consider a two-fold central extension of the Galilei group whose Lie algebra possesses an invariant and non-degenerate inner product. Using this inner product we define Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group. The particular extension of the Galilei group we consider is the classical double of a much studied group, the extended homogeneous Galilei group, which is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure of the doubly extended Galilei group, and quantise the Chern-Simons theory using a Hamiltonian approach. Many aspects of the quantum theory are determined by the quantum double of the extended homogenous Galilei group, or Galilei double for short. We study the representation theory of the Galilei double, explain how associated braid group representations account for the topological interactions in the theory, and briefly comment on an associated non-commutative Galilean spacetime.Comment: 38 pages, 1 figure, references update

On resonances and bound states of the 't Hooft-Polyakov monopole

We present a systematic approach to the linearised Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral properties. We show that a quaternionic formulation allows for a compact and efficient treatment of the linearised equations in the BPS limit of vanishing Higgs self-coupling, and use it to study both scattering and bound states. We focus on the sector of vanishing generalised angular momentum and analyse it numerically, putting zero-energy bound states, Coulomb bound states and infinitely many Feshbach resonances into a coherent picture. We also consider the linearised Yang-Mills-Higgs equations with non-vanishing Higgs self-coupling and confirm the occurrence of Feshbach resonances in this situation.Comment: 33 pages, 7 figure

Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent bundle of the Poincar\'e group, and coupled minimally to the Chern-Simons gauge field. We apply this description of spatial infinity to open universes of general genus and with an arbitrary number of massive spinning particles. Using results of [9] we give a finite dimensional description of the phase space and determine its symplectic structure. In the special case of a genus zero universe with spinless particles, we compare our result to the symplectic structure computed by Matschull in the metric formulation of (2+1)-dimensional gravity. We comment on the quantisation of the phase space and derive a quantisation condition for the total mass and spin of an open universe.Comment: 44 pages, 3 eps figure

Calculation of the nucleon axial charge in lattice QCD

Protons and neutrons have a rich structure in terms of their constituents, the quarks and gluons. Understanding this structure requires solving Quantum Chromodynamics (QCD). However QCD is extremely complicated, so we must numerically solve the equations of QCD using a method known as lattice QCD. Here we describe a typical lattice QCD calculation by examining our recent computation of the nucleon axial charge.Comment: Prepared for Scientific Discovery through Advanced Computing (SciDAC 2006), Denver, Colorado, June 25-29 200

Nucleon structure in the chiral regime with domain wall fermions on an improved staggered sea

Moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon are presented from a preliminary analysis of lattice results using pion masses down to 359 MeV. The twist two matrix elements are calculated using a mixed action of domain wall valence quarks and asqtad staggered sea quarks and are renormalized perturbatively. Several observables are extrapolated to the physical limit using chiral perturbation theory. Results are compared with experimental moments of quark distributions and electromagnetic form factors and phenomenologically determined generalized form factors, and the implications on the transverse structure and spin content of the nucleon are discussed.Comment: Talks of J.W. Negele and D.B. Renner at Lattice 200

The principle of relative locality

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.Comment: 12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III mad

Distribution Amplitudes of Pseudoscalar Mesons

We present results for the first two moments of the distribution amplitudes of pseudoscalar mesons. Using two flavors of non-perturbatively improved clover fermions and non-perturbative renormalization of the matrix elements we perform both chiral and continuum extrapolations and compare with recent results from models and experiments.Comment: 7 pages, 4 figures, based on presentation at Lattice 200