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Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda

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Harald W. Griesshammer (George Washington U.)

Nuclear Theory · Submitted 27 Jan 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A ground state exists only in the range $0.366\ldots\ge\xi\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

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arXiv ID2401.15402 (version 2)
Pith IDQOKN7RJH, Pith's permanent record of this paper and its review
CitationHarald W. Griesshammer (George Washington U.). "Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda." arXiv:2401.15402 (2024). https://pith.science/paper/QOKN7RJH
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,366 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.38 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $\xi:=2r_0/a$ once $|r_0|$ is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. At leading order, no three-body interaction is needed. A ground state exists only in the range $0.366\ldots\ge\xi\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. background 0.92 0.15 0.16 asserted 1.00
s1 Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $\xi:=2r_0/a$ once $|r_0|$ is chosen as base unit. background 0.64 0.31 0.13 asserted 1.00
s2 This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. contribution 0.96 0.65 0.04 asserted 0.80
s3 At leading order, no three-body interaction is needed. result 0.99 0.65 0.19 asserted 1.00
s4 A ground state exists only in the range $0.366\ldots\ge\xi\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$. result 1.00 0.72 0.38 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 0.67.

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $\xi:=2r_0/a$ once $|r_0|$ is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. At leading order, no three-body interaction is needed. A ground state exists only in the range $0.366\ldots\ge\xi\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 13 sentences without a confident label

Uses the method or tool of 1 paper
  • Using an idea by Gattobigio [ref] , the trajectories are in this form parametrised with residuals of $≪10^-3$ by the $7$ constants of table [ref] via [equation]

    More on the universal equation for Efimov states · A Curated Selection of Results · 0.93

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