Isoscalar electromagnetic form factors of the nucleon in $N_\mathrm{f} = 2 + 1$ lattice QCD

TL;DR

This study computes the isoscalar electromagnetic form factors of the nucleon using $N_f=2+1$ lattice QCD, employing advanced techniques to accurately include disconnected quark contributions and reduce excited-state contamination.

Contribution

It provides the first comprehensive lattice QCD calculation of isoscalar nucleon form factors including disconnected diagrams with improved statistical methods.

Findings

Disconnected contributions significantly affect the form factors.

Multiple source-sink separations help estimate excited-state effects.

Clear signals obtained for all form factors including disconnected diagrams.

Abstract

We present results for the isoscalar electromagnetic form factors of the nucleon computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_\mathrm{f} = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. For the computation of the quark-disconnected diagrams, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results.