Directly measure staggered hairpin parameters governing taste-symmetry breaking in η-meson channels

Measure the taste-symmetry-breaking hairpin parameters δ_KS(A) and δ_KS(V) associated with the axial-vector and vector tastes in staggered-fermion computations, which enter η-meson mass splittings and have not been directly determined due to the computational cost of disconnected diagrams.

Background

The authors discuss taste-symmetry breaking in staggered fermion simulations, where pseudo-scalar meson masses differ by taste due to lattice artifacts. For η-meson tastes, additional parameters δ_KS(ξ) appear: δ_KS(T)=0 within SO(4) symmetry, δ_KS(I) comes from the chiral anomaly, and δ_KS(A), δ_KS(V) are hairpin parameters.

While Δ_KS(ξ) splittings are empirically characterized, the hairpin parameters δ_KS(A) and δ_KS(V) have not been directly measured because they require disconnected contractions, which are computationally demanding. Their determination would clarify the taste-breaking structure and inform continuum extrapolations and model-based taste improvements.

References

These have never been measured directly, since the disconnected contributions are computationally demanding.

— High precision calculation of the hadronic vacuum polarisation contribution to the muon anomaly  (2407.10913 - Boccaletti et al., 2024) in Supplementary Information, Subsection "Taste violation" (label se:tavi)