Understanding Parton Distributions from Lattice QCD: Present Limitations and Future Promise

This talk will explain how ground state matrix elements specifying moments of quark density and spin distributions in the nucleon have been calculated in full QCD, show how physical extrapolation to the chiral limit including the physics of the pion cloud resolves previous apparent conflicts with experiment, and describe the computational resources required for a definitive comparison with experiment.Comment: Proceedings of Ferrara Workshop on the QCD Structure of the Nucleon 10 pages, 6 figure

Insight into the Role of Instantons and their Zero Modes from Lattice QCD

Evidence from lattice QCD calculations is presented showing that instantons and their associated zero modes play a major role in the physics of light hadrons and the propagation of light quarks in the QCD vacuum.Comment: Proceedings of KEK Tanashi Symposium. 8 pages LaTe

Understanding Hadron Structure Using Lattice QCD

Numerical evaluation of the path integral for QCD on a discrete space-time lattice has been used to calculate ground state matrix elements specifying moments of quark density and spin distributions. This talk will explain how these matrix elements have been calculated in full QCD using dynamical quarks, show how physical extrapolation to the chiral limit including the physics of the pion cloud resolves previous apparent conflicts with experiment, and describe the computational resources required for a definitive comparison with experiment.Comment: 8 pages, 7 figures, using BoxedEPS and espcrc1 macros; Invited Talk at Third International Conference on Perspectives in Hadronic Physics, Trieste; email correspondenc to [email protected]

The Quark Structure of Pentaquarks

Motivated by the possible observation of the $\Theta^+(1530)$, we study the quark structure of pentaquark states in quenched lattice QCD. The complete set of 19 local sources that have the proper symmetry for positive or negative parity isoscalar pentaquarks is constructed, as well as a nonlocal source composed of two displaced ``good'' diquarks. Quantitative structure information is determined from diagonalizing the 19-dimensional correlation matrix and from calculating the overlaps of sources with the lattice eigenstates. The volume dependence of the overlap is studied to differentiate between scattering and localized resonant states. The positive parity state has a small component of two ``good'' diquarks, and its energy is too much higher than the negative parity state to be a candidate for the $\Theta^+(1530)$.Comment: 6 pages, 3 figures Lattice 2005: Hadron Spectrum and Quark Masse

Incommensurate nematic fluctuations in the two-dimensional Hubbard model

We analyze effective d-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive d-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the d-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.Comment: 8 pages, 4 figures; figures improve

Interplay between spin density wave and π\pi phase shifted superconductivity in the Fe pnictide superconductors

We explore if the phase separation or coexistence of the spin density wave (SDW) and superconductivity (SC) states has any relation to the incommensurability of the SDW in the Fe pnictide superconductors. A systematic method of determining the phase separation or coexistence was employed by computing the anisotropy coefficient $\beta$ from the the 4th order terms of the Ginzburg--Landau (GL) expansion of the free energy close to the tricritical/tetracritical point. It was complemented by the self-consistent numerical iterations of the gap equations to map out the boundaries between the phase separation and coexistence of the SDW and SC phases, and between commensurate (C) and incommensurate (IC) SDW in the temperature--doping plane. Our principal results for the sign reversed $s$-wave pairing SC, in terms of the multicritical temperature, $T_c$, the phase separation/coexistence boundary between the SDW and SC, $T^*$, and the boundary between C/IC SDW, $T_M^*$, are: (a) IC-SDW and SC coexist for $T_c < T^*$ and phase separate otherwise, (b) SDW takes the C form for $T_c>T_M^*$ and IC form for $T_c<T_M^*$, and (c) the thermodynamic first order phase transition intervenes in between the C-SDW and IC-SDW boundary for large $T_M^0$, where $T_M^0$ is the SDW transition temperature at zero doping, $T^*=0.35 ~T_M^0$ and $T_M^*=0.56\ T_M^0$. The intervention makes the phase diagram more complicated than previously reported. By contrast no coexistence was found for the equal sign pairing SC. These results will be compared with the experimental reports in the Fe pnictide superconductors.Comment: 9 pages, 4 figures, Submitted to Phys.Rev.