Relativistic-invariant formulation of the NREFT three-particle quantization condition

Müller, Fabian; Pang, Jin-Yi; Rusetsky, Akaki; Wu, Jiajun

doi:10.1007/jhep02(2022)158

Cited by 30 publications

(24 citation statements)

References 86 publications

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“…It might be thought problematic that a lower cutoff is required for the nondegenerate theory-it certainly conflicts with the usual notion of a UV cutoff that one can send arbitrarily large, a point stressed recently in Ref. [25]. This is why we have also called H (i) a "transition function," because, in all derivations in the RFT approach, it has the effect of transitioning the two-particle amplitude that appears in the expressions between the two-particle K matrix K 2 at threshold (where H (i) = 1) and the two-particle amplitude M 2 far below threshold (where H (i) = 0).…”

Section: Cutoff Functionmentioning

confidence: 99%

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Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Blanton,

Romero-López,

Sharpe

2021

Preprint

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Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different ("2+1" systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two-and three-particle interactions predicted by chiral perturbation theory.

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Section: Cutoff Functionmentioning

confidence: 99%

“…[13]). We also note that a Lorentz-invariant extension of the NREFT formalism has recently been obtained [25]. In this work we follow the RFT approach.…”

Section: Introductionmentioning

confidence: 99%

Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Blanton,

Romero-López,

Sharpe

2021

Preprint

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“…Simulating quantum systems in finite volume (FV), such as a cubic box with periodic boundary conditions, is a well established theoretical approach to extract information about them, going back to the early work of Lüscher [1,2,3] who showed that the real-world (i.e., infinite-volume) properties of a the system are encoded in how its (discrete) energy levels change as the size of the volume is varied. The method has become a standard approach for example in Lattice Quantum Chromodynamics (LQCD) to extract scattering information for hadronic systems, and extending it in different directions, in particular to three-body systems, is an area of active research [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Moreover, few-body approaches formulated in FV can be used to match and extrapolate LQCD results to an effective field theory (EFT) description [21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Efficient few-body calculations in finite volume

König

2023

J. Phys.: Conf. Ser.

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Simulating quantum systems in a finite volume is a powerful theoretical tool to extract information about them. Real-world properties of the system are encoded in how its discrete energy levels change with the size of the volume. This approach is relevant not only for nuclear physics, where lattice methods for few- and many-nucleon states complement phenomenological shell-model descriptions and ab initio calculations of atomic nuclei based on harmonic oscillator expansions, but also for other fields such as simulations of cold atomic systems. This contribution presents recent progress concerning finite-volume simulations of few-body systems. In particular, it discusses details regarding the efficient numerical implementation of separable interactions and it presents eigenvector continuation as a method for performing robust and efficient volume extrapolations.

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“…In particular, three conceptually equivalent formulations of the three-body quantization condition (an equation that connects the finite-volume energy spectrum with the infinite-volume observables in the three-particle system) have been proposed -the socalled RFT [9,11], NREFT [19,20] and FVU [21,58] approaches. A Lorentz-invariant formulation of the NREFT approach was suggested recently [46], and a three-body analog of the Lellouch-Lüscher formula, which relates the three-body decay amplitudes, measured in a finite and in the infinite volume, has been derived [59,60]. For a more detailed overview, we refer the reader to the two recent reviews on the subject [61,62].…”

Section: Introductionmentioning

confidence: 99%

Spurious poles in a finite volume

Pang,

Ebert,

Hammer

et al. 2022

Preprint

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Using effective-range expansion for the two-body amplitudes may generate spurious subthreshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size L. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in Ref. [1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion.

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Relativistic-invariant formulation of the NREFT three-particle quantization condition

Cited by 30 publications

References 86 publications

Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Efficient few-body calculations in finite volume

Spurious poles in a finite volume

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