The string tension in the maximally Abelian gauge after smoothing

We apply smoothing to SU(2) lattice field configurations in 3+1 dimensions before fixing to the maximally Abelian gauge. The Abelian projected string tension is shown to be stable under this, whilst the monopole string tension declines by O(30%). Blocking of the SU(2) fields reduces this effect, but the use of extended monopole definitions does not. We discuss these results in the context of additional confining excitations in the U(1) vacuum.Comment: LATTICE98(confine

On the Phase Diagram of the SU(2) Adjoint Higgs Model in 2+1 Dimensions

The phase diagram is investigated for SU(2) lattice gauge theory in d=3, coupled to adjoint scalars. For small values of the quartic scalar coupling, lambda, the transition separating Higgs and confinement phases is found to be first-order, in agreement with earlier work by Nadkarni. The surface of second-order transitions conjectured by Nadkarni, however, is shown instead to correspond to crossover behaviour. This conclusion is based on a finite size analysis of the scalar mass and susceptibility. The nature of the phase transition at the termination of first-order behaviour is investigated and we find evidence for a critical point at which the scalar mass vanishes. The photon mass and confining string tension are measured and are found to be negligibly small in the Higgs phase. This is correlated with the very small density of magnetic monopoles in the Higgs phase. The string tension and photon mass rise rapidly as the crossover is traversed towards the symmetric phase.Comment: LaTeX. Replaced with version to be published in Physics Letters B. Minor changes onl

Monopole clusters, Z(2) vortices and confinement in SU(2)

We extend our previous study of magnetic monopole currents in the maximally Abelian gauge [hep-lat/9712003] to larger lattices at small lattice spacings (20^4 at beta = 2.5 and 32^4 at beta = 2.5115). We confirm that at these weak couplings there continues to be one monopole cluster that is very much longer than the rest and that the string tension, K, is entirely due to it. The remaining clusters are compact objects whose population as a function of radius follows a power law that deviates from the scale invariant form, but much too weakly to suggest a link with the analytically calculable size distribution of small instantons. We also search for traces of Z(2) vortices in the Abelian projected fields; either as closed loops of `magnetic' flux or through appropriate correlations amongst the monopoles. We find, by direct calculation, that there is no confining condensate of such flux loops. We also find, through the calculation of doubly charged Wilson loops within the monopole fields, that there is no suppression of the q=2 effective string tension out to at distances of at least r ~ 1.6/sqrt{K}, suggesting that if there are any vortices they are not encoded in the monopole fields.Comment: 26 pages of LaTeX and PostScript figure

Vortex critical behavior at the de-confinement phase transition

The de-confinement phase transition in SU(2) Yang-Mills theory is revisited in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axis are studied. Using the percolation cumulant, the temperature for the percolation transition is seen to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.Comment: 4 pages, 4 PS figures, using revtex4, paragraph and refs added, typo correcte

Vortex structures in pure SU(3) lattice gauge theory

The structures of confining vortices which underlie pure SU(3) Yang-Mills theory are studied by means of lattice gauge theory. Vortices and Z_3 monopoles are defined as dynamical degrees of freedom of the Z_3 gauge theory which emerges by center gauge fixing and by subsequent center projection. It is observed for the first time for the case of SU(3) that these degrees of freedom are sensible in the continuum limit: the planar vortex density and the monopole density properly scales with the lattice spacing. By contrast to earlier findings concerning the gauge group SU(2), the effective vortex theory only reproduces 62% of the full string tension. On the other hand, however, the removal of the vortices from the lattice configurations yields ensembles with vanishing string tension. SU(3) vortex matter which originates from Laplacian center gauge fixing is also discussed. Although these vortices recover the full string tension, they lack a direct interpretation as physical degrees of freedom in the continuum limit.Comment: 25 pages, 13 ps figures, improved presentation, results unchange

Meson Cloud of the Nucleon in Polarized Semi-Inclusive Deep-Inelastic Scattering

We investigate the possibility of identifying an explicit pionic component of the nucleon through measurements of polarized $\Delta^{++}$ baryon fragments produced in deep-inelastic leptoproduction off polarized protons, which may help to identify the physical mechanism responsible for the breaking of the Gottfried sum rule. The pion-exchange model predicts highly correlated polarizations of the $\Delta^{++}$ and target proton, in marked contrast with the competing diquark fragmentation process. Measurement of asymmetries in polarized $\Lambda$ production may also reveal the presence of a kaon cloud in the nucleon.Comment: 23 pages REVTeX, 7 uuencoded figures, accepted for publication in Zeit. Phys.

Observing Long Colour Flux Tubes in SU(2) Lattice Gauge Theory

We present results of a high statistics study of the chromo field distribution between static quarks in SU(2) gauge theory on lattices of volumes 16^4, 32^4, and 48^3*64, with physical extent ranging from 1.3 fm up to 2.7 fm at beta=2.5, beta=2.635, and beta=2.74. We establish string formation over physical distances as large as 2 fm. The results are tested against Michael's sum rules. A detailed investigation of the transverse action and energy flux tube profiles is provided. As a by-product, we obtain the static lattice potential in unpreceded accuracy.Comment: 66 pages, 29 figures, uuencoded latex file with epsfigures (450 K), supplementary full colour figures are available via ftp, CERN-TH.7413/94 (extended version

Matter degrees of freedom and string breaking in Abelian projected quenched SU(2) QCD

In the Abelian projection the Yang--Mills theory contains Abelian gauge fields (diagonal degrees of freedom) and the Abelian matter fields (off-diagonal degrees) described by a complicated action. The matter fields are essential for the breaking of the adjoint string. We obtain numerically the effective action of the Abelian gauge and the Abelian matter fields in quenched SU(2) QCD and show that the Abelian matter fields provide an essential contribution to the total action even in the infrared region. We also observe the breaking of an Abelian analog of the adjoint string using Abelian operators. We show that the adjoint string tension is dominated by the Abelian and the monopole contributions similarly to the case of the fundamental particles. We conclude that the adjoint string breaking can successfully be described in the Abelian projection formalism.Comment: 16 pages, 10 figures, 2 table

The Hyperfine Spin Splittings In Heavy Quarkonia

The hyperfine spin splittings in heavy quarkonia are studied using the recently developed renormalization group improved spin-spin potential which is independent of the scale parameter $\mu$. The calculated energy difference between the $J/\psi$ and the $\eta_c$ fits the experimental data well, while the predicted energy difference $\Delta M_p$ between the center of the gravity of $1^3P_{0,1,2}$ states and the $1^1P_1$ state of charmonium has the correct sign but is somewhat larger than the experimental data. This is not surprising since there are several other contributions to $\Delta M_p$, which we discuss, that are of comparable size ($\sim 1$ MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the $\psi'-\eta_c'$, $\Upsilon(1S)-\eta_b$, $\Upsilon(2S)-\eta_b'$, and $B_c^*-B_c$ are also predicted.Comment: 17 page

Abelian Monopole and Center Vortex Views at the Multi-Instanton Gas

We consider full non-Abelian, Abelian and center projected lattice field configurations built up from random instanton gas configurations in the continuum. We study the instanton contribution to the $\bar{Q}Q$ force with respect to ({\it i}) instanton density dependence, ({\it ii}) Casimir scaling and ({\it iii}) whether various versions of Abelian dominance hold. We check that the dilute gas formulation for the interaction potential gives an reliable approximation only for densities small compared to the phenomenological value. We find that Casimir scaling does not hold, confirming earlier statements in the literature. We show that the lattice used to discretize the instanton gas configurations has to be sufficiently coarse ($a \approx 2\bar{\rho}$ compared with the instanton size $\bar{\rho}$) such that maximal Abelian gauge projection and center projection as well as the monopole gas contribution to the $\bar{Q}Q$ force reproduce the non-Abelian instanton-mediated force in the intermediate range of linear quasi-confinement. We demonstrate that monopole clustering also depends critically on the discretization scale confirming earlier findings based on monopole blocking.Comment: 21 pages, 22 Postscript figure