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Chiral two-loop pion-pion scattering parameters from crossing-symmetric constraints

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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G. Wanders (Institut de physique théorique, Université de Lausanne)

High Energy Physics - Phenomenology · Submitted 15 May 1997

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

The authors' main claim Reliable predictions are obtained for three two-loop parameters.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-ph/9705323 (version 4)
Pith IDT3JEYD7Q, Pith's permanent record of this paper and its review
CitationG. Wanders (Institut de physique th\'eorique, Universit\'e de Lausanne). "Chiral two-loop pion-pion scattering parameters from crossing-symmetric constraints." arXiv:hep-ph/9705323 (1997). https://pith.science/paper/T3JEYD7Q
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The compiled record

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,506 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.84 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.81 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

Constraints on the parameters in the one- and two-loop pion-pion scattering amplitudes of standard chiral perturbation theory are obtained from explicitly crossing-symmetric sum rules. These constraints are based on a matching of the chiral amplitudes and the physical amplitudes at the symmetry point of the Mandelstam plane. The integrals over absorptive parts appearing in the sum rules are decomposed into crossing-symmetric low- and high-energy components and the chiral parameters are finally related to high-energy absorptive parts. A first application uses a simple model of these absorptive parts. The sensitivity of the results to the choice of the energy separating high and low energies is examined with care. Weak dependence on this energy is obtained as long as it stays below ~560 MeV. Reliable predictions are obtained for three two-loop parameters.

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 Constraints on the parameters in the one- and two-loop pion-pion scattering amplitudes of standard chiral perturbation theory are obtained from explicitly crossing-symmetric sum rules. contribution 0.86 0.87 0.27 asserted 1.00
s1 These constraints are based on a matching of the chiral amplitudes and the physical amplitudes at the symmetry point of the Mandelstam plane. method 0.99 0.75 0.06 asserted 1.00
s2 The integrals over absorptive parts appearing in the sum rules are decomposed into crossing-symmetric low- and high-energy components and the chiral parameters are finally related to high-energy absorptive parts. method 0.99 0.88 0.13 asserted 1.00
s3 A first application uses a simple model of these absorptive parts. method 0.84 0.85 0.03 asserted 0.93
s4 The sensitivity of the results to the choice of the energy separating high and low energies is examined with care. method 0.67 0.92 0.05 asserted 0.75
s5 Weak dependence on this energy is obtained as long as it stays below ~560 MeV. result 0.93 0.93 0.15 asserted 0.99
s6 Reliable predictions are obtained for three two-loop parameters. result 1.00 0.91 0.71 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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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

Constraints on the parameters in the one- and two-loop pion-pion scattering amplitudes of standard chiral perturbation theory are obtained from explicitly crossing-symmetric sum rules. These constraints are based on a matching of the chiral amplitudes and the physical amplitudes at the symmetry point of the Mandelstam plane. The integrals over absorptive parts appearing in the sum rules are decomposed into crossing-symmetric low- and high-energy components and the chiral parameters are finally related to high-energy absorptive parts. A first application uses a simple model of these absorptive parts. The sensitivity of the results to the choice of the energy separating high and low energies is examined with care. Weak dependence on this energy is obtained as long as it stays below ~560 MeV. Reliable predictions are obtained for three two-loop parameters.

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