Particle theory

Abstract:

We calculate the string tension and part of the mass spectrum of SU(4) and SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine these new results with older results for Nc=2, . . . ,5 so as to obtain more accurate extrapolations to Nc=∞. The qualitative conclusions of the earlier work are unchanged: SU(Nc∞) theories in 2+1 dimensions are linearly confining as N c→∞ the limit is achieved by keeping g2Nc fixed; SU(3), and even SU(2), are "close" to SU(∞). We obtain more convincing evidence than before that the leading large-Nc correction is O(1/N c2). We look for the multiplication of states that one expects in simple flux loop models of glueballs, but find no evidence for this. © 2002 The American Physical Society.

Abstract:

For many event-shape observables, the most difficult part of a resummation in the Born limit is the analytical treatment of the observable's dependence on multiple emissions, which is required at single logarithmic accuracy. We present a general numerical method, suitable for a large class of event shapes, which allows the resummation specifically of these single logarithms. It is applied to the case of the thrust major and the oblateness, which have so far defied analytical resummation and to the two-jet rate in the Durham algorithm, for which only a subset of the single logs had up to now been calculated. © SISSA/ISAS 2002.

Abstract:

The spectrum of glueballs in 2 +1 dimensions is calculated within an extended class of Isgur-Paton flux tube models and compared to lattice calculations of the low-lying SU(N≥2) glueball mass spectrum. Our modifications of the model include a string curvature term and a new way of dealing with the short-distance cutoff. We find that the generic model is remarkably successful at reproducing the positive charge conjugation, C = +, sector of the spectrum. The only large (and robust) discrepancy involves the 0-+ state, raising the interesting possibility that the lattice spin identification is mistaken and that this state is in fact 4-+. Additionally, the Isgur-Paton model does not incorporate any mechanism for splitting C= - from C=+ (in contrast with the case in 3 + 1 dimensions), while the "observed" spectrum does show a substantial splitting. We explore several modifications of the model in an attempt to incorporate this physics in a natural way. At the qualitative level we find that this constrains our choice to the picture in which the C= ± splitting is driven by mixing with new states built on closed loops of adjoint flux. However, a detailed numerical comparison suggests that a model incorporating an additional direct mixing between loops of opposite orientation is likely to work better, and that, in any case, a nonzero curvature term will be required. We also point out that a characteristic of any string model of glueballs is that the SU(N →∞) mass spectrum will consist of multiple towers of states that are scaled up copies of each other. To test this will require a lattice mass spectrum that extends to somewhat larger masses than currently available. © 2002 The American Physical Society.

Abstract:

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SV(Nc) gauge theories with Nc=2, 3, 4 and 5 colors. We define a fermionic topological charge from the zero modes of this operator and show that, as Nc grows, any disagreement with the topological charge obtained by cooling the fields becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about ρ≃2.5a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger Nc. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N c and is consistent with disappearing entirely in the limit of N c = ∞. We find that this is not simply due to the observed disappearance of small instantons at larger Nc. © 2002 The American Physical Society.

Abstract: