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

TL;DR

This paper examines the impact of excited state contaminations on the calculation of nucleon sigma-terms using $Nf=2+1+1$ twisted mass fermions, highlighting significant challenges in controlling systematic errors.

Contribution

It provides a detailed analysis of excited state effects in nucleon sigma-term computations with twisted mass fermions, emphasizing the importance of addressing these contaminations.

Findings

Excited state effects can be as large as 40% for strange sigma-terms.

Even with 1.5 fm source-sink separation, excited states may not be fully under control.

Disconnected contributions are efficiently evaluated using stochastic methods for twisted mass fermions.

Abstract

We investigate excited state contaminations in a direct computation of the nucleon $\sigma$-terms. This is an important source of systematic effects that needs to be controlled besides the light quark mass dependence and lattice artefacts. We use maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. Employing an efficient stochastic evaluation of the disconnected contribution available for twisted mass fermions, we show that the effect of excited states is large in particular for the strange $\sigma$-terms, where it can be as big as $O(\gtrsim 40%$). This leads to the unfortunate conclusion that even with a source-sink separation of $\sim 1.5 \fm$ and a good statistical accuracy it is not clear, whether excited state effects are under control for this quantity.