Vortex dominance of the 0+ and 2+ glueball mass in SU(2) lattice gauge theory

Abstract

The c-vortex ensembles are constructed by means of the recently proposed cooling method which gradually removes the SU (2)/Z 2 coset fields from the SU (2) lattice configurations and which thus reveals the Z 2 vortex vacuum texture. Using Teper's blocking method, the screening masses of the 0 + and the 2 + glueball is calculated from these vortex ensembles and compared with the masses obtained from full configurations. The masses of either case agree within the achieved numerical accuracy of 10%. As a byproduct, we find that the overlaps of the Teper operators with the glueball wavefunctions are significantly larger in the case of the c-vortex ensembles. * Supported in part by Graduiertenkolleg Hadronen und Kerne.PACS: 11.15.Ha 12.38.Aw keywords: confinement, vortex dominance, glueball mass, SU(2) lattice gauge theory. 1Introduction. The idea that the center part of the SU(N) gauge configurations are important for the confinement of quarks dates back to the late seventies [1]. Indeed, the proposal that the vortex free energy serves as an order parameter for quark (de-)confinement was recently confirmed in the case of a SU(2) gauge group by a large scale lattice simulation [2]. Subsequently, Mach and collaborators explicitly constructed a vortex signature of the Yang-Mills vacuum from gauge invariant variables [3]. It was observed at that time that random fluctuations of the vortex structure disorders the Wilson loop and, hence, provides quark confinement. With the increase of the computer performance in the mid eighties, many research efforts were devoted to substantiate this idea on a quantitative level [4,5]. One finds that projecting the full lattice configurations onto its vortex content reproduces the string tension of the static quark anti-quark potential. Recently, it was pointed out that not only the asymptotic behavior of the potential but also the short range part which is due to gluon exchange is reproduced if the plaquette is used for a definition of the vortex ensemble [6]. Moreover, the properties of the vortices arising from the plaquette projection technique strongly depend on the size of the lattice spacing thus rendering a continuum interpretation of the latter vortices cumbersome [6].

SU(2) Abelian Projected Action for Renormalisation Group Flows

“…Though the mass of the off-diagonal gauge field is gauge dependent, it does not imply that this energy scale itself is a gauge artifact. The value of M AD obtained in [16] is, within error margins, not far from the lightest glueball mass in SU (2) YM, m 0 ++ G ∼ 1.67 GeV [17]. In SU (3) YM the value of m 0 ++ G is in the same range, m 0 ++ G = 1.6−1.8 GeV [18].…”

Gauge invariant Z(2) vortex vacuum textures and the SU(2) gluon condensate

“…After the major part of the confining vortices is removed by cooling, it remains to be clarified which specific physical significance could be assigned to the exposed Z(2) vortex ensembles. Following the original version of this paper, it was observed in [27] that the masses of the low-lying glueballs, O + and 2 + , are rather insensitive against the here proposed cooling. Below, we will give further arguments supporting the idea that these configurations are not just lattice artefacts but play an important rôle in the non-perturbative physics at intermediate distances dealt with in the OPE.…”

Singular gauge potentials and the gluon condensate at zero temperature

“…This question has been answered by a comparison of the lowest glueball states in uncooled and coset-cooled gauge field onfigurations reported in Ref. [7]. …”

“…This question has been answered by a comparison of the lowest glueball states in uncooled and coset-cooled gauge field onfigurations reported in Ref. [7]. For β = 2.3, 2.4 and 2.5 on a 8 3 × 16 lattice the lowest O + glueball state (with mass m O + = 1.67(11) GeV) and the lowest 2 + glueball state (m 2 + = 2.30(8) GeV), have been identified first on uncooled configurations.…”