Origin of the L_s-dependent discrepancy in partially-quenched Wilson-kernel DWF ensembles

Determine whether the small but statistically significant difference in the extrapolated L_s→∞ condensate Φ_∞ observed between auxiliary-field ensembles generated with L_s(sea)=24 and L_s(sea)=32 for the 2+1-dimensional N=1 Thirring model with Wilson-kernel domain wall fermions at β=0.34 and ma=0.005 on a 16^3 lattice—when measured with L_s(valence) up to 120—arises from insufficient statistics or from a genuine feedback effect due to generating the ensemble at finite L_s in the sea sector.

Background

The paper employs a partially-quenched strategy in which auxiliary-field ensembles are generated at fixed L_s(sea)=24 and, for a check case, L_s(sea)=32, while measurements of the U(2) order-parameter condensate i⟨ψ̄γ3ψ⟩ are performed with larger L_s(valence) up to 120 to extrapolate to L_s→∞.

A comparison at β=0.34 and ma=0.005 shows that although S_bose agrees between L_s(sea)=24 and 32, the extrapolated condensate Φ∞ differs slightly, with Φ∞ from the L_s(sea)=32 ensemble smaller than that from L_s(sea)=24 at L_s(valence)=120. This raises the question whether the observed difference is a statistical fluctuation due to limited statistics or an intrinsic systematic effect from partial quenching (a feedback effect of finite L_s in the sea).

Clarifying the origin of this discrepancy is important to validate the partially-quenched methodology and to assess potential systematic errors in extracting the critical behavior of the model.