Topological Susceptibility in SU(3) Gauge Theory

We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find $r_0^4\chi =0.059(3)$, which corresponds to $\chi =(191\pm 5\mathrm{M}\mathrm{e}\mathrm{V}{)}^4$ if $F_K$ is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the ${\eta }^{\prime }$.

Figure 1

The topological susceptibility, in units of $r_0^{-4}$, as a function of the linear lattice size, in fm, at $\beta =6.0$.

Figure 2

Histogram for the distribution of the topological charge $Q$ from the lattice $D$.

Figure 3

Continuum extrapolation of the adimensional product $r_0^4\chi$. The $s=0.0$ and $s=0.4$ data sets are represented by black circles and white squares, respectively. The dashed lines represent the results of the combined fit described in the text. The filled diamond at $a=0$ is the extrapolated value in the continuum limit.