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Three-body resonances in the $\varphi^4$ theory

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arxiv 2211.05605 v2 pith:OLKQZ37B submitted 2022-11-10 hep-lat

Marco Garofalo , Maxim Mai , Fernando Romero-López , Akaki Rusetsky , Carsten Urbach This is my paper · ORCID
classification hep-lat
keywords theorythree-bodyapproachcomplexdeterminefindfinite-volumelattice
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the properties of three-body resonances using a lattice complex scalar $\varphi^4$ theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy-plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

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Cited by 3 Pith papers

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    hep-lat 2025-10 conditional novelty 8.0 of 10

    Lattice QCD plus three-body scattering formalism yields a π(1300)-like pole at (1169±46)−i(62−62+168) MeV, consistent with experiment.

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    The I=2 three-pion spectrum from lattice QCD is described by a repulsive rho-pi S-wave interaction, consistent with a leading-order effective Lagrangian.

  3. Universal parameters of the $\Lambda(1380)$, the $\Lambda(1405)$ and their isospin partners from a combined analysis of Lattice QCD and experimental results

    hep-ph 2025-07 conditional novelty 6.0 of 10

    A combined global fit of lattice QCD spectra and experimental Kbar N data within chiral unitary approaches gives pole positions for the Lambda(1380) and Lambda(1405) at physical and lattice quark masses, with systemat...

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