The topological susceptibility in ‘ full ’ ( UK ) QCD

We report first calculations of the topological susceptibility measured using the field theoretic method on SU(3) gauge configurations produced by the UKQCD collaboration with two flavours of dynamical, improved, Wilson fermions. Using three ensembles with matched lattice spacing but differing sea quark mass we find that hybrid Monte Carlo simulation appears to explore the topological sectors efficiently, and a topological susceptibility consistent with increasing linearly with the quark mass. The latest UKQCD runs generate SU(3) field configurations using a Wilson gauge action coupled to n f = 2 flavours of Wilson sea quarks, non–perturbatively improved such that the leading order discretisation errors in spectral quantities should be O(a 2). In dynamical simulations the lattice spacing, a, is influenced by the gauge coupling, β, and the quark mass parameter, κ. The ensembles studied represent three points on a trajectory in the (β, κ) space of (approximately) constant a and physical volume (V a 4 = 16 3 .32a 4) [1]. [The lattice spacing has been defined from the static inter–quark potential, using r 0 = 0.49 fm [2].] Along such trajectories, however , there is a change in chiral behaviour as seen in the pseudoscalar to vector mesonic mass ratio in Table 1. [Dimensionless lattice quantities are denoted with circumflexes throughout.] We measure the topological charge density on the lattice using the field theoretic operator ˆ Q(n) = 1 2 × 1 16 ε ± µνστ Tr U µν (n)U στ (n), (1) symmetrised such that ε ± µνσ,−τ = −ε ± µνσ,+τ etc. to improve the signal on moderately cooled lattices. The topological charge, ˆ Q, and susceptibility , ˆ χ, are then ˆ Q = 1 32π 2 n ˆ Q(n) ˆ χ = ˆ Q 2 V. (2) Although formally in the weak coupling limitˆQ is related to that of the continuum byˆQ = a 4 Q + O(a 6), the prefactors of the higher order terms typically have momenta on the scale of 1/a such that they are O(1), andˆQ becomes increasingly dominated by ultraviolet noise near the continuum limit. It is also subject to a multiplicative renormalisation that reduces the signal at the β couplings accessible to simulation. An established, and well understood, procedure to extract the topological signal is to cool the configurations prior to measuringˆQ. This locally smoothens the lattice fields to remove the ultraviolet fluctuations, and drives the renormal-isation constant to unity. We …