arXiv subjects
Publications and source records attributed to Howard D. Trottier.
We calculate the potential between adjoint sources in $SU(2)$ pure gauge theory in three dimensions. We investigate whether the potential saturates at large separations due to the creation of a pair of gluelumps, colour-singlet states formed when glue binds to an adjoint source.
Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in three dimensions. Monopoles are computed by Abelian projection in several gauges, including the maximal Abelian gauge. The number $N_m$ of extended monopoles in a cube of size $m^3$ (in lattice units) is defined as the number of elementary ($1^3$) monopoles minus antimonopoles in the cube ($m=1,2,\ldots$). The distribution of $1^3$ monopoles in the nonlocal maximal Abelian gauge is shown to be essentially random, while nonscaling of the density of $1^3$ monopoles in some local gauges, which has been previously observed, is shown to be mainly due to strong short-distance correlations. The density of extended monopoles in local gauges is studied as a function of $β$ for monopoles of fixed physical ``size'' ($m / β= {\rm fixed}$); the degree of scale violation is found to decrease substantially as the monopole size is increased. The possibility therefore remains that long distance properties of monopoles in local gauges may be relevant to continuum physics, such as confinement.
The effect of cooling on a number of observables is calculated in SU(2) lattice gauge theory. The static quark-antiquark potential and spin-dependent interactions are studied, and the topological charge is monitored. The chiral symmetry breaking order parameter $\langle \overlineχχ\rangle$ and meson correlators are calculated using staggered fermions. Interactions on the distance scale of a few lattice spacings are found to be essentially eliminated by cooling, including the spin-dependent potentials. $\langle \overlineχχ\rangle$ and meson correlators up to time separations of several lattice spacings relax very quickly to their free-field values. At larger times, there is evidence of a difference between the pseudoscalar and vector channels. A fit to the pseudoscalar correlation function yields ``mass'' values about $2/3$ (in lattice units) of the uncooled masses. These results raise the question of how to reconcile the large-time behavior of the hadron correlators with the fact that the spin-dependent potentials and $\langle \overlineχχ\rangle$ essentially disappear (in lattice units) after only a small amount of cooling.
A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorization theorem.
A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorization theorem. The bound obtained here adds to the limited information so far available on the color-octet mechanism for $P$-wave quarkonium production.
The role of monopoles in the confining behavior of compact lattice $QED_3$ is studied using an adiabatic cooling method. Monopole-antimonopole pairs with large separation suvive cooling and the presence or absence of such plasma monopoles provides a useful classification of the lattice gauge field configurations at large $β$. By calculating observables in subsets of gauge field configurations which contain or do not contain plasma monopoles it is seen that, in compact $QED_3$, monopoles dominate the long distance physics, e.g., the string tension, linear confining potential and dynamical mass generation. On the other hand, the spin-spin interaction is essentially unaffected by monopoles.
Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\cal A}_j$ as a function of representation are made. It is found that ${\cal A}_j \approx {\rm constant}$, to about 10\%. Results are consistent with a connection between the string tension $σ_j$ and ${\cal A}_j$ suggested by a simplified flux-tube model, $σ_j = g^2 j(j+1) / (2 {\cal A}_j)$ [$g$ is the gauge coupling], given that $σ_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED$_3$ are also measured. It is found that the string tension scales as the squared-charge and the flux-tube cross-section is independent of charge to good approximation. These SU(2) and U(1) simulations lend some support, albeit indirectly, to a conjecture that the dual superconductor mechanism underlies confinement in compact gauge theories in both three and four dimensions.
The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.