Particle theory

Abstract:

We present results of a numerical calculation of the chiral condensate in quenched SU(2) lattice gauge theory. The calculation proceeds by evaluating the spectral density distribution function for small eigenvalues on both the original lattice and after a factor-of-two blocking. It is performed on lattices as large as 204 and for couplings as small as β = 4/g2 = 2.6. The fitted values of the condensate as a function of β show good evidence for scaling and universality when compared with string tension measurements at the same value. At the smallest lattice spacings considered, we find evidence that a separation of length scales between ultraviolet fluctuations and those responsible for chiral symmetry breaking has occurred. A more qualitative study yields a significant correlation between the small modes |n〉 responsible for the non-zero value of 〈ψψ〉 and topological activity as revealed by the expectation value 〈n|γ5 ⊗ 1|n〉, and hence provides evidence for a topological origin of chiral symmetry breaking. Our interpretation is supported by a subsidiary calculation of the topological susceptibility of the vacuum. © 1990.

Abstract:

We have carried out a simulation of QCD using the hybrid-molecular-dynamics algorithm with two flavors of staggered quarks. The spectrum was calculated for 6g2=5.6 and dynamical quark masses amq=0.025 and 0.01. Lattice sizes of 124, 123×24, and 164 were used to generate the gauge configurations. Hadron propagators were calculated with both staggered and Wilson quarks on doubled or quadrupled latices. Finite-size effects are visible on the smaller lattices. Some improvement in the to-nucleon mass ratio and chiral symmetry is seen as compared to previous calculations, but, as in most lattice calculations, the proton-to mass ratio remains larger than in the real world and the proton splitting is too small. © 1990 The American Physical Society.