Towards the finite-volume spectrum of the Roper resonance

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.

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“…(for more comparisons, see ref. [113]). This is a noteworthy result considering that the present formalism is much simpler.…”

Section: N π Channelmentioning

confidence: 99%

Particle-dimer approach for the Roper resonance in a finite volume

Severt¹,

Mai

Meißner

2023

J. High Energ. Phys.

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Three-body resonances in the φ4 theory

Garofalo¹,

Mai

Romero-López

et al. 2023

J. High Energ. Phys.

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We study the properties of three-body resonances using a lattice complex scalar φ4 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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Towards the finite-volume spectrum of the Roper resonance

Cited by 2 publications

References 30 publications

Particle-dimer approach for the Roper resonance in a finite volume

Particle-dimer approach for the Roper resonance in a finite volume

Three-body resonances in the φ4 theory

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