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

TL;DR

This paper presents a lattice QCD variational analysis to extract nucleon weak matrix elements, addressing excited state contamination and comparing preliminary results with chiral perturbation theory predictions.

Contribution

It introduces a variational approach using nucleon-like and nucleon-pion-like operators to improve the extraction of nucleon matrix elements in lattice QCD.

Findings

First preliminary results of Nπ to N matrix elements obtained.

Comparison with chiral perturbation theory shows qualitative agreement.

Addresses excited state contamination in nucleon matrix element calculations.

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 $\langle N\pi| \mathcal{J}| N \rangle $, 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 $T=2L\approx 4.8~\mathrm{fm}$.