ω Meson from Lattice QCD

Area of Science:

• Nuclear Physics
• Quantum Chromodynamics (QCD)
• Hadron Spectroscopy

Background:

• Many excited hadron states decay into three-hadron final states.
• Understanding these states from first principles Quantum Chromodynamics (QCD) is crucial.
• This requires lattice QCD calculations and advanced three-body formalisms.

Purpose of the Study:

• To perform the first lattice QCD calculation of the omega (ω) meson resonance parameters.
• To update the theoretical formalism by matching to effective field theories.
• To determine the pole position and estimate the ω-ρ mass difference.

Main Methods:

• Utilizing lattice QCD with one-, two-, and three-meson interpolators.
• Employing a reliable three-body formalism to connect finite-volume spectra to scattering amplitudes.
• Matching the formalism to effective field theories for improved accuracy.

Main Results:

• The first calculation of the omega (ω) meson pole position from lattice QCD.
• The calculated pole position is $\sqrt{s_ω} = (778.0(11.2) - i3.0(5))\text{ MeV}$, showing good agreement with experimental values.
• An estimated ω-ρ mass difference of 29(15) MeV was obtained.

Conclusions:

• This work provides a significant step towards understanding three-hadron final states from first principles.
• The results validate the lattice QCD approach for determining resonance parameters.
• Future studies can build upon this formalism to investigate other hadronic resonances.