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We present a lattice-QCD based analysis of the nucleon sigma terms using gauge ensembles with $N_f = 2 + 1$ flavors of ${\cal O}(a)$-improved Wilson fermions, with a complete error budget concerning excited-state contaminations, chiral extrapolation as well as finite-size and lattice spacing effects. We compute the sigma terms determined directly from the matrix elements of the scalar currents. For the pion nucleon sigma term, we obtain $\sigma_{\pi N} = (43.6\pm3.8)$ MeV, where the error includes all systematics. The tension with extractions based on dispersion theory persists at the 3-$\sigma$ level. For the strange sigma term, we obtain a non-zero value, $\sigma_s=(27.1\pm9.8)$ MeV.

We present an analysis of the pion-nucleon sigma term on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions. We perform a chiral interpolation based on ensembles with pion masses ranging from 130 MeV to roughly 350 MeV. The analysis covers four lattice spacings between $a\approx [0.05 \, \rm{fm}\ldots 0.09\, \rm{fm}]$, allowing for an estimate of systematics associated with lattice artefacts., Talk presented at the 39th International Symposium on Lattice Field Theory (Lattice 2022), 8-13 August, 2022, Bonn, Germany

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the $��N��^*$ transition form factors from lattice data. A counterpart of the L��scher approach for the matrix elements of unstable states is formulated. In particular, we thoroughly discuss various kinematic settings, which are used in the calculation of the above matrix element on the lattice. The emerging L��scher-Lellouch factor and the analytic continuation of the matrix elements into the complex plane are also considered in detail. A full group-theoretical analysis of the problem is made, including the partial-wave mixing and projecting out the invariant form factors from data., 29 pages, 5 figures. Right-hand side of Eq. (4.13) is corrected by the normalization factor $V^{-1/2}$ and all related formulas namely, Eqs. (4.15), (4.16), (4,17), (4.21), (4.36), (5.1), (5.3) accordingly