Spin on the Lattice

Abstract

I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using domain wall fermions are also discussed.Understanding the basic properties of matter requires the understanding of the nucleon structure. Quantum Chromodynamics (QCD) is the theory describing strong interactions and hence is responsible for the properties of the nuclear matter. Although QCD has been around for more than twenty years, its non-perturbative nature is an obstacle to the direct connection of low energy physics to quarks and gluons, the fundamental degrees of freedom of the theory. Unlike QED, non-perturbative techniques had to be developed in order to understand the QCD predictions at low energies. The lattice formulation of QCD is both a non-perturbative way to define the theory and a very powerful tool in understanding its properties.Deep inelastic scattering of leptons on nucleons has been an important tool in understanding the structure of hadrons. Over the last few decades experiments at SLAC, Fermilab, CERN, DESY, and more recently at RHIC and JLAB, have measured the quark and gluon light cone distribution functions of the nucleon. These experiments have substantially advanced our knowledge of the properties of hadrons. However, we would also like to study how this observed rich phenomenology arises form first principles, i.e. QCD. With todays advances in computer technology, algorithms, and recent developments in lattice regularization of fermions, lattice calculations can complement the experimental effort and promote our understanding of the non-perturbative nature of QCD.

Automated Lattice Perturbation Theory

“…There is a wide variety of nonperturbative methods and a full discussion is beyond the scope of these proceedings, but a partial list includes nonperturbative tuning via physical quantities or dispersion relations (see, for example, [2]); imposing Ward identities or chiral symmetry relations [3]; and step-scaling methods, which have been applied to the Schrödinger functional [4], off-shell Green functions (the "Rome-Southampton method") [5], physical quantities [6] and gradient flow smearing procedures [7].…”

Lattice matrix elements and CP violation inB andK physics: Status and outlook

“…First, recent studies of renormalization group-improved gauge actions in the context of domain wall fermions appear very promising in significant improvements in chiral symmetry (which was already remarkably good) [96]. Efforts are also underway towards creating a large ensemble of gauge configurations with dynamical (2 flavor) domain wall quarks [16] with lattice spacing ∼ (2 GeV −1 ).…”

Calculation of moments of structure functions

“…These have much better chiral properties than Wilson fermions and so are more suitable for investigating small quark masses. In [59], v 2b is computed on a 16 3 × 32[×16] lattice at a −1 ∼ 1.3GeV. Thus the lowest pion mass there, (am ps ) 2 ∼ 0.1, corresponds to about (r 0 m ps ) 2 ∼ 1 in Fig.…”