Investigation of pion-nucleon contributions to nucleon matrix elements

We investigate contributions of excited states to nucleon matrix elements computed in lattice QCD by employing, in addition to the standard nucleon interpolating operator, pion-nucleon ($\pi$-$N$) operators. We solve a generalized eigenvalue problem (GEVP) to obtain an optimal interpolating operator that minimizes overlap with the $\pi$-$N$ states. We derive a variant of the standard application of the GEVP method, which allows for constructing 3-point correlation functions using the optimized interpolating operator without requiring the computationally demanding combination that includes $\pi$-$N$ operators in both sink and source. We extract nucleon matrix elements using two twisted mass fermion ensembles, one ensemble generated using pion mass of 346 MeV and one ensemble tuned to reproduce the physical value of the pion mass. Especially, we determine the isoscalar and isovector scalar, pseudoscalar, vector, axial, and tensor matrix elements. We include results obtained using a range of kinematic setups, including momentum in the sink. Our results using this variational approach are compared with previous results obtained using the same ensembles and multi-state fits without GEVP improvement. We find that for the physical mass point ensemble, the improvement, in terms of suppression of excited states using this method, is most significant for the case of the matrix elements of the isovector axial and pseudoscalar currents.