Sigma terms and strangeness content of the nucleon with $N_f=2+1+1$ twisted mass fermions

TL;DR

This paper computes the scalar quark content of the nucleon using twisted mass fermions with dynamical light, strange, and charm quarks, providing a benchmark for future detailed studies.

Contribution

It demonstrates the feasibility of accurately calculating nucleon scalar matrix elements for light and strange quarks with twisted mass fermions, serving as a benchmark for future work.

Findings

Good statistical accuracy for light and strange quark densities

Only an upper bound obtained for charm quark content

Serves as a benchmark for future systematic studies

Abstract

We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound can be provided. The present calculation which is performed at only one value of the lattice spacing and pion mass serves as a benchmark for a future more systematic computation of the scalar quark content of the nucleon.