# Feynman-Hellmann theorem for resonances and the quest for QCD exotica

## TL;DR

This paper extends the Feynman-Hellmann theorem to resonance states in quantum field theory, providing a new criterion to identify exotic hadronic states in QCD, supported by theoretical calculations and lattice data analysis.

## Contribution

It introduces a generalized Feynman-Hellmann theorem for resonances and proposes a criterion to detect QCD exotica, validated through Chiral Perturbation Theory and lattice data.

## Key findings

- Resonance states can be analyzed using the generalized Feynman-Hellmann theorem.
- Most hadronic states studied are consistent with quark-model predictions.
- Corrections to quark-model states are significant but do not indicate exotic nature.

## Abstract

The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible.