Excited states and precision results for nucleon charges and form factors

TL;DR

This paper reviews the challenges of extracting nucleon matrix elements due to excited state contamination and discusses how including multihadron states in analyses can significantly alter results, with implications for phenomenology.

Contribution

The paper provides a comprehensive review of the impact of multihadron excited states on nucleon matrix element calculations and highlights the importance of including these states for accurate results.

Findings

Including multihadron states can change nucleon matrix element results significantly.

Chiral perturbation theory supports large effects from excited states in key form factors.

Analysis suggests substantial effects in the neutron EDM and sigma term calculations.

Abstract

The exponentially falling signal-to-noise ratio in all nucleon correlation functions, and the presence of towers of multihadron excited states with relatively small mass gaps makes extraction of matrix elements of various operators within the ground state nucleon challenging. Theoretically, the allowed positive parity states with the smallest mass gaps are the $N(\bm p)\pi(-\bm p)$, $N(\bm 0)\pi(\bm 0)\pi(\bm 0)$, $N(\bm p)\pi(\bm 0)$, $N(\bm 0)\pi(\bm p),\ \ldots$, states. A priori, the contribution of these states arises at one loop in chiral perturbation theory ($\chi$PT), however, in many cases the contributions are enhanced. In this talk, I will review four such cases: the correlation functions from which the axial form factors, electric and magnetic form factors, the $\Theta$-term contribution to neutron electric dipole moment (nEDM), and the pion-nucleon sigma term are extracted. Including appropriate multihadron states in the analysis can lead to significantly different results compared to standard analyses with the mass gaps taken from fits to 2-point functions. The $\chi$PT case for $N \pi$ states is the most clear in the axial/pseudoscalar form factors which need to satisfy the PCAC relation between them. Our analyses, supported by $\chi$PT, suggests similarly large effects in the calculations of the $\Theta$-term and the pion-nucleon sigma term that have significant phenomenological implications.