Bound states in the 
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-matrix formalism for the three-body scattering

Dawid, Sebastian M.; Szczepaniak, Adam P.

doi:10.1103/physrevd.103.014009

Cited by 17 publications

(19 citation statements)

References 60 publications

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“…Two main relativistic on-shell 3 → 3 scattering formalisms have been developed and applied to a range of physical problems: (a) the relativistic EFT (RFET) established by Hansen, Sharpe, and Briceño in Refs. [409,[414][415][416], and (b) the S-matrix unitarity, also referred to as the B-matrix approach, built by Mai et al [410,417,418] and the JPAC group [54,419,420]. All of these works have been shown to be equivalent both in their infinite-volume [421] and finite-volume [422] versions.…”

Section: → 3 Scatteringmentioning

confidence: 99%

“…Using the notation of Refs. [420,421], the elastic 3 → 3 scattering amplitude, M, is defined as the three-body element of the T matrix. It is convenient to work with the unsymmetrized isobar-spectator amplitude [M p p ] m ; m , written in the so called (p m ) basis in which it can be treated as an infinite-dimensional matrix in the isobars angular momentum space.…”

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

“…The B-matrix equation produces a convenient parametrization of the three-body amplitude, reducing it to a three-dimensional integral equation through the isobar assumption. The formalism can accommodate distinguishable spinless particles and was generalized to include the two-body channels [420].…”

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

“…In Refs. [419,420] the domain of integration is restricted to physical values of energies. In principle, this requires one to include only the experimentally accessible sub-channel 2 → 2 amplitudes without the need for additional assumptions.…”

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

“…In Ref. [420] the authors perform a comparable analysis, using a model of relativistic three-body scattering with a bound state in the two-body subchannel. They focus on the contact interaction approximation in which the exact solution of the model can be achieved, being effectively a series of bubble diagrams.…”

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

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Novel approaches in Hadron Spectroscopy

Albaladejo,

Bibrzycki,

Dawid

et al. 2021

Preprint

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The last two decades have witnessed the discovery of a myriad of new and unexpected hadrons. The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the states requires a parallel theoretical effort. To make full use of available and forthcoming data, a careful amplitude modeling is required, together with a sound treatment of the statistical uncertainties, and a systematic survey of the model dependencies. We review the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy.

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Section: → 3 Scatteringmentioning

confidence: 99%

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

Section: Relativistic Three-body Formalismsmentioning

confidence: 99%

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Novel approaches in Hadron Spectroscopy

Albaladejo,

Bibrzycki,

Dawid

et al. 2021

Preprint

Self Cite

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Relativistic N-particle energy shift in finite volume

Romero-López

Rusetsky

Schlage

et al. 2021

J. High Energ. Phys.

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We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L−6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex φ4 theory.

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Finite-volume scattering on the left-hand cut

Baião Raposo,

Hansen

2024

J. High Energ. Phys.

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The two-particle finite-volume scattering formalism derived by Lüscher and generalized in many subsequent works does not hold for energies far enough below the two-particle threshold to reach the nearest left-hand cut. The breakdown of the formalism is signaled by the fact that a real scattering amplitude is predicted in a regime where it should be complex. In this work, we address this limitation by deriving an extended formalism that includes the nearest branch cut, arising from single particle exchange. We focus on two-nucleon (NN → NN) scattering, for which the cut arises from pion exchange, but give expressions for any system with a single channel of identical particles. The new result takes the form of a modified quantization condition that can be used to constrain an intermediate K-matrix in which the cut is removed. In a second step, integral equations, also derived in this work, must be used to convert the K-matrix to the physical scattering amplitude. We also show how the new formalism reduces to the standard approach when the N → Nπ coupling is set to zero.

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Bound states in the B -matrix formalism for the three-body scattering

Cited by 17 publications

References 60 publications

Novel approaches in Hadron Spectroscopy

Novel approaches in Hadron Spectroscopy

Relativistic N-particle energy shift in finite volume

Finite-volume scattering on the left-hand cut

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