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

Abstract

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 $N\pi$ 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 $(qqq)(\bar{q}q)$-operators (nucleon-pion-like) where we report for the first time some preliminary results of $⟨N\pi |\mathcal{J}|N⟩$, modulo some kinematic and volume factors, and we compare the results against ChPT. This pilot study is performed on a CLS ensemble with $N_f=3$, $m_{\pi }\approx 420\mathrm{MeV}$, $a\approx 0.1\mathrm{fm}$ and $T=2L\approx 4.8\mathrm{fm}$.

Comments: Proceedings for the EuroPLEx Final Conference, 11-15 September 2023, Humboldt University of Berlin