Excited-State Effects in Nucleon Sigma Terms from a Variational Analysis

We investigate excited-state effects in nucleon sigma-terms in lattice QCD using twisted-mass clover-improved fermion ensembles. We study correlation functions with nucleon and multihadron nucleon-$\sigma$-meson interpolating operators. The analysis is performed using three gauge ensembles, including one ensemble simulated with two degenerate light, a strange, and a charm quark with quark masses tuned to approximately their physical value. We solve the generalized eigenvalue problem that arises from the matrix of correlators and show that the three-point function for the light sigma-term obtained using the optimal linear combination of interpolating operators has substantially reduced time dependence without loss of statistical precision. We apply Laplace filtering and investigate residual excited-state contributions in the extraction of ${\sigma }_{\pi N}$. Using the same optimal linear combination of correlators as for ${\sigma }_{\pi N}$ for the strange sigma-term we also observe suppressed excited state contributions over an extended range of source–sink time separations. For the charm sigma-term, we observe negligible time dependence within the large statistical uncertainties, and these improvements show no significant effect.