arXiv subjects
Publications and source records attributed to T. Draper.
We report our calculation of the pion decay constant $f_π$, the axial renormalization constant $Z_A$, and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched $20^4$ lattice at $a=0.148$ fm using tree level tadpole improved gauge action. The smallest pion mass we reach is about 280 MeV. The lattice size is about 4 times the Compton wavelength of the lowest mass pion.
We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized.
We reply to Nathan Isgur's critique that is directed at some of the conclusions drawn from the lattice simulation of valence QCD, regarding the valence quark model and effective chiral theories.
A valence QCD theory is developed to study the valence quark properties of hadrons. To keep only the valence degrees of freedom, the pair creation through the Z graphs is deleted in the connected insertions; whereas, the sea quarks are eliminated in the disconnected insertions. This is achieved with a new ``valence QCD'' lagrangian where the action in the time direction is modified so that the particle and antiparticle decouple. The theory has the vector and axial $U(2N_F)$ symmetry in the particle-antiparticle space. Through lattice simulation, it appears that this is dynamically broken down to $U_q(N_F) \times U_{\bar{q}}(N_F)$. Furthermore, the lattice simulation reveals spin degeneracy in the hadron masses and SU(6) relations in the ratios of $F_A/D_A, F_S/D_S$, and $μ^n/μ^p$. This leads to an approximate $U_q(2N_F) \times U_{\bar{q}}(2N_F)$ symmetry which is the basis for the valence quark model. We find that the masses of N, $Δ, ρ, π, a_1$, and $a_0$ all drop precipitously compared to their counterparts in the quenched QCD calculation. This is interpreted as due to the disapperance of the `constituent' quark mass which is dynamically generated through tadpole diagrams. Form the near degeneracy between N and $Δ$ for the quark masses we have studied (ranging from one to four times the strange mass), we conclude that the origin of the hyper-fine splitting in the baryon is largely attibuted to the Goldstone boson exchanges between the quarks. These are the consequences of lacking chiral symmetry in valence QCD. We discuss its implication on the models of hadrons.
We describe a lattice calculation of the matrix elements relevant for glueball production in $J / ψ$ radiative decays. The techniques for such a calculation on anisotropic lattices with an improved action are outlined. We present preliminary results showing the efficacy of the computational method.
Results for the isovector axial form factors of the proton from a lattice QCD calculation are presented for both point-split and local currents. They are obtained on a quenched $16^{3} \times 24$ lattice at $β= 6.0$ with Wilson fermions for a range of quark masses from strange to charm. We determine the finite lattice renormalization for both the local and point-split currents of heavy quarks. Results extrapolated to the chiral limit show that the $q^2$ dependence of the axial form factor agrees reasonably well with experiment. The axial coupling constant $g_A$ calculated for the local and the point-split currents is about 6\% and 12\% smaller than the experimental value respectively.