Toward $N$ to $N\pi$ matrix elements from lattice QCD

Abstract

QCD matrix elements of axial and vector currents between nucleons are required for the Monte Carlo reconstruction of the energy of neutrinos that are detected in long baseline oscillation experiments in the quasi-elastic regime. The cleanest approach for determining the axial matrix elements is lattice QCD. However, the extraction of these from the corresponding correlation functions is complicated by very large excited state contributions, that are related to transitions from the nucleon to a nucleon-pion pair. In this pilot study with a pion mass $m_{\pi }=429\mathrm{MeV}$, we demonstrate for the first time that these contributions can be removed by including five-(anti)quark operators into the basis of interpolators used to create the nucleon. The same techniques will be needed to compute transition matrix elements between the nucleon and nucleon-pion scattering states that are relevant in the resonance production regime.

arXiv comment5 pages + Supplemental Material, 5 figures

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• FLAG Review 2024
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• Investigation of pion-nucleon contributions to nucleon matrix elements
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• Moments of Nucleon Unpolarized, Polarized, and Transversity Parton Distribution Functions from Lattice QCD at the Physical Point
• Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing $\pi N$-state contamination