# Constraining the hadronic spectrum through QCD thermodynamics on the lattice

## TL;DR

This study uses lattice QCD simulations with imaginary strangeness chemical potentials to investigate the hadronic spectrum, revealing the need for additional strange resonances beyond established states to match thermodynamic data.

## Contribution

It introduces a novel lattice QCD approach at imaginary chemical potentials to constrain the hadronic spectrum, highlighting missing states in the HRG model.

## Key findings

- Established states are insufficient to match lattice results.
- Additional PDG or Quark Model states are needed for agreement.
- Interactions beyond HRG may be required in the strange meson sector.

## Abstract

Fluctuations of conserved charges allow to study the chemical composition of hadronic matter. A comparison between lattice simulations and the Hadron Resonance Gas (HRG) model suggested the existence of missing strange resonances. To clarify this issue we calculate the partial pressures of mesons and baryons with different strangeness quantum numbers using lattice simulations in the confined phase of QCD. In order to make this calculation feasible, we perform simulations at imaginary strangeness chemical potentials. We systematically study the effect of different hadronic spectra on thermodynamic observables in the HRG model and compare to lattice QCD results. We show that, for each hadronic sector, the well established states are not enough in order to have agreement with the lattice results. Additional states, either listed in the Particle Data Group booklet (PDG) but not well established, or predicted by the Quark Model (QM), are necessary in order to reproduce the lattice data. For mesons, it appears that the PDG and the quark model do not list enough strange mesons, or that, in this sector, interactions beyond those included in the HRG model are needed to reproduce the lattice QCD results.