The thick-or fat-center-vortices model has been applied to a calculation of the potentials between static sources of various SU (4) representations. For intermediate distances, a linear potential is obtained. For this region the string tensions agree qualitatively with both flux tube counting and Casimir scaling, even though for some representations it favors flux tube counting more. In addition, our results confirm the existence of two different string tensions for non-zero 4-ality representations at large distances. In this area, zero 4-ality representations are screened. In our computations, we have used only the first non-trivial vortex of SU (4).
We study the potential between static SU(4) sources using the Model of Thick
Center Vortices. Such vortices are characterized by the center elements
$z_1=\mathrm i$ and $z_2=z_1^2$. Fitting the ratios of string tensions to those
obtained in Monte-Carlo calculations of lattice QCD we get $f_2>f_1^2$, where
$f_n$ is the probability that a vortex of type $n$ is piercing a plaquette.
Because of $z_2=z_1^2$ vortices of type two are overlapping vortices of type
one. Therefore, $f_2>f_1^2$ corresponds to the existence of an attractive force
between vortices of type one
The thick center vortex model reproduces important aspects of the potentials between static quark sources as seen in lattice Yang-Mills calculations: Both the intermediate distance behavior, governed by Casimir scaling, as well as the long distance behavior, governed by N-ality, are obtained. However, when a fixed vortex profile is used, these two distance regimes do not connect naturally to each other. The transition in general violates concavity constraints on the potential, especially for higher representations of the gauge group. We demonstrate how this issue can be alleviated when the vortex profile is allowed to fluctuate within this simple model.
The short distance potentials between heavy SU(3) and SU(4) sources are
calculated by increasing the role of vortex fluxes piercing Wilson loops with
contributions close to the trivial center element and by fluctuating the vortex
core size in the model of thick center vortices. By this method, a Coulombic
potential consistent with Casimir scaling is obtained. In addition, all other
features of the potential including a linear intermediate potential in
agreement with Casimir scaling and a large distance potential proportional to
the $N$-ality of the representation are restored. Therefore, the model of thick
center vortices may be used as a phenomenological model, which is able to
describe the potential for all regimes.Comment: 9 pages and 6 figure
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.