Can the Feynman-Hellmann theorem be used to separate the connected- and disconnected-diagram contributions to the nucleon sigma term ?

TL;DR

This paper questions the reliability of using the Feynman-Hellmann theorem to separately estimate connected and disconnected contributions to the nucleon sigma term in lattice QCD, highlighting potential pitfalls.

Contribution

The paper provides a theoretical analysis showing the limitations of applying the Feynman-Hellmann theorem to individual diagram contributions in QCD.

Findings

Using the theorem separately for each contribution can be misleading.

The theorem reliably applies only to the total nucleon sigma term.

Caution is advised when interpreting separated contributions in lattice QCD studies.

Abstract

In recent lattice QCD studies, the Feynman-Hellmann theorem is often used to estimate separate contributions of the connected and disconnected diagrams to the nucleon sigma term. We demonstrate through a simple analysis within an effective model of QCD why this could be dangerous although the theorem is naturally expected to hold for the sum of the two contributions, i.e. the net nucleon sigma term.