Lattice Quantum Chromodynamics with Applications to Thermodynamics of Hadronic Matter and Properties of Hadrons

D. K. Sinclair, J.-F. Lagae, and G. T. Bodwin, Argonne National Laboratory
J. B. Kogut, University of Illinois
S. Kim, Sejong University

Research Objectives

Application of improved actions for lattice quantum chromodynamics (QCD) to the study of the transition of hadronic matter to a quark-gluon plasma at high temperature. Development of such improved actions (with particular emphasis on the fermionic part of the action). Application of nonrelativistic QCD methods to studies of heavy quarkonium.

Computational Approach

QCD is simulated on a discrete space-time lattice (lattice QCD) by formulating it as a molecular-dynamics problem and solving its time evolution numerically. A stochastic driving term is applied periodically to ensure ergodicity and rapid progress through phase space. The Dirac operator that describes quark propagation is inverted numerically using a conjugate gradient method. These computations have been ported to the T3E using the natural parallelism associated with the lattice and the locality of its interactions.

Accomplishments

We are studying the properties of a new action for the quarks in lattice QCD -- domain-wall fermions -- where the 4-dimensional quarks are the boundary values of a 5-dimensional fermion field. This formulation formally has exact chiral symmetry as the 5th dimension becomes infinite. We are studying the low-lying eigenmodes of this theory at high temperatures, and the way the Atiyah-Singer index theorem is realized as the extent of the 5th dimension is increased. In addition we are studying mesonic excitations of the plasma phase. Preliminary results look promising.

We have continued our simulations of lattice QCD, with an extra 4-fermion term allowing us to use massless quarks. This has enabled us to identify the 2-flavor finite-temperature phase transition and confirm that it is second order. The masslessness of the quarks has enabled us to extract preliminary values of one of the critical indices at this transition, and to get a clearer picture of the behavior of mesonic excitations as we cross this transition.

Our earlier calculations of the decay rates of S- and P-wave bottomonium have been extended to include the effects of light "sea" quarks. Earlier calculations in the quenched approximation predicted decay rates appreciably lower than experiment. Preliminary results indicate that the inclusion of light quarks is adequate to correct this.

Last year we introduced a new action for staggered quarks. Preliminary indications on small lattices indicated that this greatly reduced the flavor symmetry breaking at modest lattice spacing. We have now performed extensive calculations on a larger lattice, indicating that it does indeed considerably reduce flavor symmetry breaking, and we have quantified this improvement.

Lowest 2 eigenvalues of the domain-wall Dirac operator as functions of the 5th dimension on a configuration of topological charge 1.

Finally, we have extended our studies of the low-lying eigenmodes of the staggered quark Dirac operator at high temperatures to larger lattices, and are checking the Atiyah-Singer index theorem, measuring the topological charge with an improved cooling scheme, and observing how the chirality density of the quark fields tracks the topological charge density of the gluon fields.

Significance

The finite-temperature phase transition is expected to be observed in relativistic heavy ion collider experiments. It is also important for the understanding of the early universe. These measurements also allow us to understand the underlying dynamics of QCD. Improved actions allow the use of coarser lattices, thus reducing the computing requirements for simulations. Bottomonium decay rates can be compared with experiment. We also predict the decay rates for as yet unobserved decays.

Publications

J.-F. Lagae and D. K. Sinclair, "Domain wall fermions at finite temperature," e-print hep-lat/9809134 (1998).

J. B. Kogut, J.-F. Lagae, and D. K. Sinclair, "Thermodynamics of lattice QCD with chiral four fermion interactions," Phys. Rev. D 58, 034504 (1998); e-print hep-lat/9809052.

J.-F. Lagae and D. K. Sinclair, "Improved staggered quark actions with reduced flavour symmetry violations for lattice QCD," e-print hep-lat/9806014 (1998).