Dispersive π K → π K and π π → K K ̄ amplitudes from scattering data, threshold parameters, and the lightest strange resonance κ or K 0 ∗ ( 700 )

Peláez, José R.; Rodas, Arkaitz

doi:10.1016/j.physrep.2022.03.004

Title: Dispersive $π K \to π K$ and $π π \to K \bar{K}$ amplitudes from scattering data, threshold parameters, and the lightest strange resonance $κ$ or $K_{0}^{*} (700)$

Journal Article · Fri Jul 01 00:00:00 EDT 2022 · Physics Reports

DOI:https://doi.org/10.1016/j.physrep.2022.03.004· OSTI ID:1878244

Peláez, José R.;

We discuss the simultaneous dispersive analyses of $$\pi K\to \pi K$$ and $$\pi \pi \to K \bar{K}$$ scattering data and the $$\kappa/K^*_0(700)$$ resonance. The unprecedented statistics of present and future Hadron Experiments, modern Lattice QCD calculations, and the wealth of new states and decays, require such precise and model-independent analyses to describe final state interactions. We review the existing and often conflicting data and explain in detail the derivation of the relevant dispersion relations, maximizing their applicability range. Next, we review and extend the caveats on some data, showing their inconsistency with dispersion relations. Our main result is the derivation and compilation of precise amplitude parameterizations constrained by several $$\pi K\to \pi K$$ and $$\pi \pi \to K \bar{K}$$ dispersion relations. These constrained parameterizations are easily implementable and provide the rigor and accuracy needed for modern experimental and phenomenological Hadron Physics. As applications, after reviewing their status and interest, we will provide new precise threshold and subthreshold parameters and review our dispersive determination of the controversial $$\kappa/K^*_0(700)$$ resonance and other light-strange resonances.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); Spanish Ministry of Science and Innovation; European Union (EU)

Grant/Contract Number:: SC0018416; AC05-06OR23177; PID2019-106080GB-C21; 824093

OSTI ID:: 1878244

Alternate ID(s):: OSTI ID: 1874808

Report Number(s):: JLAB-THY-20-3276; DOE/OR/23177-5068; arXiv:2010.11222; S0370157322001053; PII: S0370157322001053

Journal Information:: Physics Reports, Journal Name: Physics Reports Vol. 969 Journal Issue: C; ISSN 0370-1573

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

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Dispersive analysis of the κ / K ₀ ^* (700) meson and other light strange resonances Peláez, José R.; Rodas, Arkaitz; Ruiz de Elvira, Jacobo EPJ Web of Conferences, Vol. 212 https://doi.org/10.1051/epjconf/201921203003	journal	January 2019
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Observation of a cusp-like structure in the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> invariant mass distribution from <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> decay and determination of the ππ scattering lengths Batley, J. R.; Lazzeroni, C.; Munday, D. J. Physics Letters B, Vol. 633, Issue 2-3 https://doi.org/10.1016/j.physletb.2005.11.087	journal	February 2006
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The <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> S-wave from the <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> decay Link, J. M.; Yager, P. M.; Anjos, J. C. Physics Letters B, Vol. 681, Issue 1 https://doi.org/10.1016/j.physletb.2009.09.057	journal	October 2009
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Title: Dispersive $π K \to π K$ and $π π \to K \bar{K}$ amplitudes from scattering data, threshold parameters, and the lightest strange resonance $κ$ or $K_{0}^{*} (700)$