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

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 $π$N $σ$-term, we find that 10 $Z_2$-noise sources suffice on our sample ( about 150 independent QCD configurations at $β= 5.6$ on $16^3\times32$ with $κ_{sea} = 0.157$, equivalent to $M_π/M_ρ = 0.76(1)$), to achieve decent signals and adequate fluctuations, rather than 300 such sources as recently used in quenched simulations.