Evaluating Sea Quark Contributions to Flavour-Singlet Operators in Lattice QCD

Abstract

In a full QCD lattice study with $N_f=2$ Wilson fermions, we seek to optimize the signals for the disconnected contributions to the matrix element of flavour-singlet operators between nucleon states, which are indicative for sea quark effects. We demonstrate, in form of a fluctuation analysis to the noisy estimator technique, that -- in order to achieve a tolerable signal to noise-ratio in full QCD -- it is advantageous to work with a $Z_2$-noise source rather than to rely only on gauge invariance to cancel non-gauge-invariant background. In the case of the $\pi$N $\sigma$-term, we find that 10 $Z_2$-noise sources suffice on our sample ( about 150 independent QCD configurations at $\beta =5.6$ on $16^3\times 32$ with ${\kappa }_{sea}=0.157$, equivalent to $M_{\pi }/M_{\rho }=0.76(1)$), to achieve decent signals and adequate fluctuations, rather than 300 such sources as recently used in quenched simulations.

11 pages, uuencoded, latex and 15 postscript figures