Progress on nucleon transition matrix elements with a lattice QCD variational analysis

Nucleon weak matrix elements can be extracted from nucleon correlation functions with lattice QCD simulations. The signal-to-noise ratio prohibits the analysis at large source-sink separations and as a consequence, excited state contamination affects the extraction of the nucleon matrix elements. Chiral perturbation theory (ChPT) suggests that the dominant contamination in some of these channels is due to Nπ states where the pion carries the same momentum of the current. In this talk, we report updates on the variational analysis with $qqq$-operators (nucleon-like) and (qqq)(q̄q)-operators (nucleon-pion-like) where we report for the first time some preliminary results of Nπ| J| N, modulo some kinematic and volume factors, and we compare the results against ChPT. This pilot study is performed on a CLS ensemble with Nf=3, m_π ≈ 420~MeV, a≈ 0.1~fm and T=2L≈ 4.8~fm.