Evidence of current-enhanced excited states in lattice QCD three-point functions

Abstract

Excited-state contamination remains one of the leading sources of systematic uncertainty in the precise determination of hadron structure observables from lattice QCD. In this work, I present a general mechanism, motivated by meson dominance and implemented through the variational method, that identifies which excited states are enhanced by the choice of inserted current and kinematics. The argument is supported by numerical evidence and predictions from chiral perturbation theory across different hadronic channels, in particular in the nucleon sector, and provides both conceptual insight and practical guidance for controlling excited-state effects in hadron three-point function analyses.

Figures (7)

• Figure 1: Standard ratios in Eq. \ref{['ratiomethod']} with a pseudoscalar current insertion at non-zero momentum transfer and different source-sink separations from different lattice groups. (top left): Results from the NME Collaboration, taken from Ref. Park:2021ypf. The data are $t$- and $\tau$-dependent at different source-sink separations (different colours) and they differ from the expected nucleon matrix element (grey band), extracted using multi-state fits. (top right) and (bottom): Results from the PACS Collaboration Aoki:2025taf and ETM Collaboration Alexandrou:2020okk, respectively, exhibit similar large ESC.
• Figure 2: Ratios in Eq. \ref{['ratiomethod']} with a temporal axial-vector current insertion $\mathcal{J}=\bar{u} \gamma_4 \gamma_5 d$ at non-zero momentum transfer and different source-sink separations from different lattice groups. (top left): Results from the NME Collaboration, Ref. Park:2021ypf. (top right) and (bottom): PACS Aoki:2025taf and ETM Alexandrou:2020okk, respectively, show similarly large ESC. The grey band in the top left plot highlights the extracted nucleon matrix element.
• Figure 3: (top left) Comparison of lattice determinations of $\sigma_{\pi N}$ with $N_f=2+1$ and $N_f=2+1+1$ and phenomenological determinations from nucleon-pion scattering data. The grey band and black data represent the FLAG 2024 average. (top right) Lattice determination from the Mainz lattice group of $\sigma_{\pi N}$ on a single ensemble at $m_\pi = 200~\rm MeV$ at different source-sink separations $t$ (different colours). The grey band highlights the fitted value for $\sigma_{\pi N}$ and the black diamond is the result of a two-state fit to the summed correlator. For more details see PhysRevLett.131.261902. (bottom) Ratios in Eq. \ref{['ratiomethod']} with an isoscalar scalar current insertion at zero momentum transfer and different source-sink separations Gupta:2021ahb.
• Figure 4: GEVP-improved ratios with a pseudoscalar and temporal axial-vector current insertion at non-zero momentum transfer and different source-sink separations. (left) Results from Ref. Barca:2022uhi at $m_\pi = 429~\rm MeV$. (right) Results from the ETM collaboration in Ref. Alexandrou:2024tin at $m_\pi = 346~\rm MeV$.
• Figure 5: Comparison between standard (blue) and GEVP-improved (red) ratios in Eq. \ref{['ratiomethod']} with the isoscalar scalar current at zero momentum and source-sink separations, and at $m_\pi = 429~\rm MeV$, see Ref. Barca:2024hrl. The ESC is completely removed within statistical uncertainties. The dominant source of ESC is the $N\sigma$ state.