QCD thermodynamics with dynamical overlap fermions

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on _Nt=6$N_t=6$ and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.     

A lattice Dirac operator for QCD with light dynamical quarks

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator, typically parametrised by the residual mass, should be negligible for almost all observables if the residual mass of the Dirac operator is much smaller than the quark mass. However, maintaining a small residual mass becomes increasingly expensive as the quark mass decreases towards the physical value and the continuum limit is approached. We investigate the feasibility of using a new approximately chiral Dirac operator with a small residual mass as an alternative to overlap and domain wall fermions for lattice simulations. Our Dirac operator is constructed from a Zolotarev rational approximation for the matrix sign function that is optimal for bulk modes of the hermitian kernel Dirac operator but not for the low-lying parts of its spectrum. We test our operator on various ³²³×64${32}^3\times 64$ lattices, comparing the residual mass and the performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing and pion mass with a hyperbolic tangent operator as used by domain wall fermions. We find that our approximations have a significantly smaller residual mass than domain wall fermions at a similar computational cost, and still admit topological charge change.     

Recent advances in lattice gauge theories

Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.     

Nuclear physics from lattice QCD

We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.     

Search for the Θ1540) in lattice QCD

We report on a study of the pentaquark Θ⁺(1540), using a variety of different interpolating fields. We use chirally improved fermions in combination with Jacobi-smeared quark sources to improve the signal and get reliable results even for small quark masses. The results of our quenched calculations, which have been done on a 12³×24 lattice with a lattice spacing of a = 0.148fm, do not provide any evidence for the existence of a Θ⁺ with positive parity. We do observe, however, a signal compatible with nucleon-kaon scattering state. For the negative parity the results are inconclusive, due to the potential mixture with nucleon-kaon and N^*-kaon scattering states.     

Understanding nucleon structure using lattice simulations

This review focuses on the discussion of three key results of nucleon structure calculations on the lattice. These three results are the quark contribution to the nucleon spin, J_q, the nucleon-Δ transition form factors, and the nucleon axial coupling, g_A. The importance for phenomenology and experiment is discussed and the requirements for future simulations are pointed out.     

Highly improved lattice field-strength tensor

We derive an -improved lattice version of the continuum field-strength tensor. Discretization errors are reduced via the combination of several clover terms of various sizes, complemented by tadpole improvement. The resulting improved field-strength tensor is used to construct -improved topological charge and action operators. As a test of our improved field-strength tensor, we compare the values attained by these operators as we cool several configurations to self-duality with a previously defined highly improved action and assess the relative scale of the remaining discretization errors. We demonstrate accuracy to better than one part in 10,000.     

Roper resonance—Its static and dynamic properties from single- and double-pion production

In most investigations the Roper resonance is sensed only very indirectly via complex partial wave analyses. We find indications for its excitation in the pp→npπ⁺ reaction, where some resonance-like structure is observed in the invariant nπ⁺ mass spectrum at with a width of 150 MeV. The values fit very favorably to the most recent phase shift results as well as to the observations at BES. In near-threshold two-pion production pp→ppπ⁰π⁰ the Roper excitation and its subsequent decay into Nππ is the only dominant process. There we find its decay into the Nσ channel as the dominating decay process — in favor of a monopole nature of the Roper excitation.     

Latest lattice results for baryon spectroscopy

Theoretical and computational advances have enabled not only the masses of the ground states, but also some of the low-lying excited states to be calculated using Lattice Gauge Theory. In this talk, I look at recent progress aimed at understanding the spectrum of baryon excited states, including both baryons composed of the light u and d quarks, and of the heavier quarks. I then describe recent work aimed at understanding the radiative transitions between baryons, and in particular the N-Roper transition. I conclude with the prospects for future calculations.     

Transverse spin structure of hadrons from lattice QCD

This paper presents recent lattice QCD calculations of transverse spin densities of quarks in hadrons.² Based on our simulation results for the tensor generalized form factors, we find substantial correlations between spin and coordinate degrees of freedom in the nucleon and the pion. They lead to strongly distorted transverse spin densities of quarks in the nucleon and a surprisingly non-trivial transverse spin structure of the pion. Following recent arguments by Burkardt [M. Burkardt, Phys. Rev. D 72 (2005) 094020], our results imply that the Boer-Mulders function , describing correlations of the transverse spin and intrinsic transverse momentum of quarks, is large and negative for up-quarks in the proton and the π⁺. This supports the recent hypothesis that all Boer-Mulders functions are alike [arXiv:0705.1573], and also provides additional motivation for future studies of azimuthal asymmetries in πp Drell-Yan production at, e.g., COMPASS.     

What does low energy physics tell us about the zero momentum gluon propagator

The connection between QCD, a nonlocal Nambu–Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson–Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, Γ_π→γγ${\Gamma }_{\pi \to \gamma \gamma }$ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson–Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of the above scenarios. Furthermore, the nonlocal Nambu–Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.     

Exotic phases of finite temperature gauge theories

We calculate the phase diagrams at high temperature of SU(N) gauge theories with massive fermions by minimizing the one-loop effective potential. Considering fermions in the adjoint (Adj) representation at various N we observe a variety of phases when N_f2 Majorana flavours and periodic boundary conditions are applied to fermions. Also the confined phase is perturbatively accessible. For N=3, we add Fundamental (F) representation fermions with antiperiodic boundary conditions to adjoint QCD to show how the Z(3)-symmetry breaks in the confined phase.     

Pairs of chiral quarks on the lattice from staggered fermions

A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. A domain wall formulation giving a truncation of this overlap construction is also outlined.     

High-precision nonperturbative QCD

Recent advances in lattice QCD have resulted in the first simulations with realistic quark vacuum polarization. Consequently a wide variety of high-precision (few percent) nonperturbative calculations are possible now. This paper reviews the recent developments that make this possible, and presents early evidence that the era of high-precision nonperturbative QCD is at hand. It also discusses the future impact of lattice QCD on experiments, and particularly for heavy-quark physics.     

Distance preconditioning for lattice Dirac operators

We propose a preconditioning of the Dirac operator based on the factorisation of a predefined function related to the decay of the propagator with the distance. We show that it can improve the accuracy of correlators involving heavy quarks at large distances and accelerate the computation of light quark propagators.     

WChPT analysis of twisted mass lattice data

We perform a Wilson Chiral Perturbation Theory (WChPT) analysis of quenched twisted mass lattice data. The data were generated by two independent groups with three different choices for the critical mass. For one choice, the so-called pion mass definition, one observes a strong curvature for small quark masses in various mesonic observables (“bending phenomenon”). Performing a combined fit to the next-to-leading (NLO) expressions, we find that WChPT describes the data very well and the fits provide very reasonable values for the low-energy parameters.