Abstract and subjects
PoS(LATTICE2021)478 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.