Gluon contributions to the pion mass and light cone momentum fraction

We calculate the matrix elements of the gluonic contributions to the energy-momentum tensor for a pion of mass 600 < Mpi < 1100 MeV in quenched lattice QCD. We find that gluons contribute (37 +/- 8 +/- 12)% of the pion's light cone momentum. The bare matrix elements corresponding to the trace anomaly contribution to the pion mass are also obtained. The discretizations of the energy-momentum tensor we use have other promising applications, ranging from calculating the origin of hadron spin to QCD thermodynamics.Comment: 4 pages, 2 figure

Exploring quark transverse momentum distributions with lattice QCD

We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bi-local quark-quark operator connected by a straight Wilson line, allowing us to study T-even, "process-independent" TMDs. Beyond results for x-integrated TMDs and quark densities, we present a study of correlations in x and transverse momentum. Our calculations are based on domain wall valence quark propagators by the LHP collaboration calculated on top of gauge configurations provided by MILC with 2+1 flavors of asqtad-improved staggered sea quarks.Comment: 36 pages, 24 figures; revised version of May 2011, one appendix adde

Exploring the transition into the Chiral Regime of QCD using the Interacting Instanton Liquid Model

The non-perturbative quark-gluon interaction depends significantly on the value of the quark mass. In particular, in the light quark mass regime, correlations are strongly influenced by dynamics associated to chiral symmetry breaking. We use the Interacting Instanton Liquid Model (IILM) as a tool to investigate the microscopic dynamical mechanisms which underly the dependence on the quark mass and drive the transition into the chiral regime of QCD. To ensure the validity of the model, we first verify that the dependence on the quark mass for several observables calculated in the IILM agrees well with the predictions of chiral perturbation theory and with lattice simulations. We then show that a quark mass m*~80 MeV emerging naturally from the model specifies the mass scale above which the dynamics associated with low-lying eigenmodes of the Direac operator becomes sub-leading and the contribution of the fermion determinant is suppressed.Comment: contribution to XXV International Symposium on Lattice Field Theory, July 2007, Regensbur

Electromagnetic form factors of the Delta baryon

We develop a methodology that enables us to extract accurately the electromagnetic Delta form factors and their momentum dependence. We test our approach in the quenched approximation as a preparation for a study using dynamical fermions. Our calculation of the four form factors covers pion masses between about 410 MeV and 560 MeV on lattices with a size of 2.9 fm and a lattice spacing 0.09 fm. From the form factors we are able to obtain estimates of the magnetic moment and the charge radius of the Delta, which we compare to existing experimental and theoretical results.Our non-zero result for the electric quadrupole form factor signals a deformation of the Delta, pointing to an oblate charge distribution

Source Galerkin Calculations in Scalar Field Theory

In this paper, we extend previous work on scalar $\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using polynomial expansions for the generating functional $Z$, we calculate propagators and mass-gaps for a number of systems. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. The use of polynomial expansions illustrates in a clear and simple way the ideas of the Source Galerkin method. But at the same time, this choice has serious limitations. Even after exploiting symmetries, the size of calculations become prohibitive except for small systems. The calculations in this paper were made on a workstation of modest power using a fourth order polynomial expansion for lattices of size $8^2$,$4^3$,$2^4$ in $2D$, $3D$, and $4D$. In addition, we present an alternative to the Galerkin procedure that results in sparse matrices to invert.Comment: 31 pages, latex, figures separat

The N to Δ\Delta axial transition form factors in quenched and unquenched QCD

The four N to $\Delta$ axial transition form factors are evaluated using quenched QCD, using two flavors of dynamical Wilson fermions and using domain wall valence fermions on three-flavor MILC configurations for pion masses down to 360 MeV. We provide a prediction for the parity violating asymmetry as a function of $Q^2$ and examine the validity of the non-diagonal Goldberger-Treiman relation.Comment: Normalization factor in figures 3 and 4 corrected, discussion on the evaluation of the renormalized qaurk mass included, typos corrected, 7 pages, 6 figures, talk presented at the XXIV International Symposium on Lattice Field Theory, 23rd - 28th of July, 200