arXiv subjects
Publications and source records attributed to Walter Wilcox.
Direct evaluation of charged particle polarizabilities on the lattice is quite difficult. However, a short cut for charged pion polarizability - the Das, Mathur, Okubo Sum Rule - can readily be calculated using lattice techniques. A phenomenological model has been developed to fit the time behavior of the propagators in this expression. Numerical systematics are discussed and some preliminary results are presented.
Using lattice QCD on a $16^{3}\times 24$ lattice at $β=6.0$, we examine the elastic limit of charge overlap functions in the quenched approximation for the pion and rho meson; results are compared to previous direct current insertion calculations. A good signal is seen for the pion, but the electric and magnetic rho meson results are considerably noisier. We find that the pion and rho results are characterized by a monopole mass to rho mass ratio of $0.97(8)$ and $0.73(10)$, respectively. Assuming the functional form of the electric and magnetic form factors are the same, we also find a rho meson g-factor of $g=2.25(34)$, consistent with the nonrelativistic quark model.
Formulas are developed for use in lattice studies of charged hadron polarizabilities. In particular, the valence quark different-flavor component of the charged pion polarizability is examined on a $16^{3}\times 24$ lattice at $β=6.0$ using Wilson fermions. Using the elastic limit results of Part I of this series, it is concluded that this represents a small negative component of the full charged polarizabilty.
Nonzero chemical potential studies with Wilson fermions should avoid the proliferation of flavor-equivalent nucleon states encountered with staggered formulation of fermions. However, conventional wisdom has been that finite baryon density calculations with Wilson fermions will be prohibitively expensive. We demonstrate that the volume method applied to Wilson fermions gives surprisingly stable results on a small number of configurations. It is pointed out that this method may be applied to any local or nonlocal gauge invariant quantity. Some illustrative results for $<\overlineψψ>$ and $< J >$ at various values of $μ$ in a quenched lattice simulation are given.
The $πNN$ form factor $g_{πNN}(q^2)$ is obtained from a quenched lattice QCD calculation of the pseudoscalar form factor $g_P(q^2)$ of the proton with pion pole dominance. We find that $g_{πNN}(q^2)$ fitted with the monopole form agrees well with the Goldberger-Treiman relation and is much preferred over the dipole form. The monopole mass is determined to be $0.75 \pm 0.14 {\rm GeV}$ which shows that $g_{πNN}(q^2)$ is rather soft. The extrapolated $πN$ coupling constant $g_{πNN} = 12.7 \pm 2.4$ is quite consistent with the phenomenological values. We also compare $g_{πNN}(q^2)$ with the axial form factor $g_A(q^2)$ to check the pion dominance in the induced pseudoscalar form factor $h_A(q^2)$ vis à vis chiral Ward identity.
We present results towards the calculation of the pion electric form factor and structure function on a $16^3\times 24$ lattice using charge overlap. By sacrificing Fourier transform information in two directions, it is seen that the longitudinal four point function can be extracted with reasonable error bars at low momentum.
The results of a lattice simulation of time-separated charge overlap for the charged pion are discussed. The expected result $\sim {\rm exp}[-(E_q - m_π)t\,]$ for large charge density overlap time separations, $t$, is clearly visible in the Fourier transform, indicating that the elastic limit can be achieved at low to medium momentum values on present-sized lattices. The implications of this result for direct lattice simulations of hadron structure functions are discussed and a brief presentation of the lattice formalism is given.
A numerical investigation of time-separated charge overlap measurements is carried out for the pion in the context of lattice QCD using smeared Wilson fermions. The evolution of the charge distribution function is examined and the expected asymptotic time behavior $\sim e^{-(E_{q}-m_π)t}$, where $t$ represents the charge density relative time separation, is clearly visible in the Fourier transform. Values of the pion form factor are extracted using point-to-smeared correlation functions and are seen to be consistent with the expected monopole form from vector dominance. The implications of these results for hadron structure calculations is briefly discussed.
We calculate electric and magnetic form factors of protons and neutrons in quenched Monte Carlo lattice QCD on a $16^3\times 24$ lattice at $β= 6.0$ using Wilson fermions. We employ a method which characterizes one of the nucleon fields as a fixed zero-momentum secondary source. Extrapolating the overall data set to the chiral limit, we find acceptable fits for either dipole or monopole forms and extract proton and neutron magnetic moments, the magnitude of which are $10$ to $15\%$ low compared to experiment. In the extrapolation of the dipole fit of the form factors, we find that the dipole to nucleon mass ratio is about $7\%$ low compared to experiment. In addition, we obtain positive values of the neutron electric form factor, which, however, are poorly represented by a popular phenomenological form at intermediate to small $κ$ values. A zero-momentum technique for extracting hadron magnetic moments is briefly discussed and shown to yield unrealistically small magnetic moment values.