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Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the $\omega$meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the $\omega$meson at $\sqrt{s_{\omega }}=\left(778.0\right(11.2)-i3.0(5\left)\right)\mathrm{MeV}$, agrees reasonably well with experiment. In addition we provide an estimate of the $\omega -\rho$mass difference as 29(15) MeV. Published by the American Physical Society2024 

A bstract We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum. 

Abstract Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions^1–3to quantum chemistry^4–6and from atomic and molecular systems^7–9to nuclear physics^10–14. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations^15,16of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions^17,18and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations^19,20.