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 $K_{0}^{*} (700)$

Abstract

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.

Authors:

Peláez, José R.;

Publication Date:: Fri Jul 01 00:00:00 EDT 2022

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

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

OSTI Identifier:: 1878244

Alternate Identifier(s):: OSTI ID: 1874808

Report Number(s):: JLAB-THY-20-3276; DOE/OR/23177-5068; arXiv:2010.11222
Journal ID: ISSN 0370-1573; S0370157322001053; PII: S0370157322001053

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

Resource Type:: Published Article

Journal Name:: Physics Reports

Additional Journal Information:: Journal Name: Physics Reports Journal Volume: 969 Journal Issue: C; Journal ID: ISSN 0370-1573

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; meson-meson scattering; strange resonances; dispersion relations

Citation Formats


                    Peláez, José R., and Rodas, Arkaitz. 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 ).  Netherlands: N. p., 2022. 
Web.  doi:10.1016/j.physrep.2022.03.004.

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                    Peláez, José R., & Rodas, Arkaitz. 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 ).  Netherlands.  https://doi.org/10.1016/j.physrep.2022.03.004

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                    Peláez, José R., and Rodas, Arkaitz. Fri .  
"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 )".  Netherlands.  https://doi.org/10.1016/j.physrep.2022.03.004.

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@article{osti_1878244,

  title        = {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 )},

  author       = {Peláez, José R. and Rodas, Arkaitz},

  abstractNote = {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.},

  doi          = {10.1016/j.physrep.2022.03.004},

  journal      = {Physics Reports},

  number       = C,

  volume       = 969,

  place        = {Netherlands},

  year         = {Fri Jul 01 00:00:00 EDT 2022},

  month        = {Fri Jul 01 00:00:00 EDT 2022}

}

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The nature of σ, κ, <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:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <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:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
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Title: 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 )

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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 $K_{0}^{*} (700)$

Isospin violation in pion–kaon scattering
journal, March 2002

πKscattering inputs to ChPT
journal, July 2004

Chiral nonet mixing in $π K$ scattering
journal, December 2015

New Dispersion Relations in the Description of ππ Scattering Amplitudes
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Dispersion relation for hadronic light-by-light scattering: two-pion contributions
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Evidence for direct $C P$ violation in the decay $B^{\pm} \to D^{(} *^{)} K^{\pm}$ , $D \to K_{S}^{0} π^{+} π^{-}$ and measurement of the CKM phase $ϕ_{3}$
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The preliminary lattice QCD calculation of κ meson decay width
journal, January 2012

$π N$ and strangeness sigma terms at the physical point with chiral fermions
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Dispersive analysis of the γγ⁎ → ππ process
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scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors
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Nature of Light Scalar Mesons from their Large- $N_{c}$ Behavior
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Features of π Δ photoproduction at high energies
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A guide to analytic extrapolations
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Regge theory and particle physics
journal, June 1971

Lattice investigation of the scalar mesons a 0(980) and κ using four-quark operators
journal, April 2013

Dalitz plot analysis of $η_{c} \to K^{+} K^{-} η$ and $η_{c} \to K^{+} K^{-} π^{0}$ in two-photon interactions
journal, June 2014

Is $SU (2) \otimes SU (2)$ a Better Symmetry than SU(3)?
journal, March 1971

Improving the hadron physics of non-Standard-Model decays: example bounds on R-parity violation
journal, January 2013

Coupled channel analysis of JPC = 0++and 2++ isoscalar mesons with masses below 2.0 GeV
journal, January 1992

Analysis of a K -Scattering Phase Shift and Evidence for the (900) Meson
journal, September 1997

High-Precision Determination of the Pion-Nucleon $σ$ Term from Roy-Steiner Equations
journal, August 2015

Pion-Nucleon Sigma Term from Lattice QCD
journal, December 2021

Kπ scattering phase shifts determined from the reactions K+p→K+π−Δ++ and K+p→KoπoΔ++
journal, September 1971

General features of low energy Kπ scattering from physical region method
journal, October 1973

Minuit - a system for function minimization and analysis of the parameter errors and correlations
journal, December 1975

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
journal, April 2021

High statistics study of the reaction π−p→π−π+n: Apparatus, method of analysis, and general features of results at 17 GeV/c
journal, June 1974

Combined analysis of the decays τ − → K S π − ν τ and τ − → K − ην τ
journal, September 2014

Extracting the pion-nucleon sigma-term from data
journal, October 1988

$K_{0}^{⁎} (800)$ as a companion pole of $K_{0}^{⁎} (1430)$
journal, August 2016

Leading hadronic contribution to the muon magnetic moment from lattice QCD
journal, April 2021

Identification of a Scalar Glueball
journal, December 2008

Quasi-Particles and Gauge Invariance in the Theory of Superconductivity
journal, February 1960

Padé approximants and resonance poles
journal, October 2013

Baryonic Regge trajectories with analyticity constraints
journal, September 2004

Study of the elastic scaterring from the reaction K−p→K−π−pπ+ at 4.25 GeV/c incident K− momentum
journal, December 1973

The nonet of the light scalar tetraquarks: The mesons a0(980) and $K_{0}^{⁎} (800)$
journal, February 2019

Nonperturbative Approach to Effective Chiral Lagrangians and Meson Interactions
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Direct Evaluation of the Quark Content of Nucleons from Lattice QCD at the Physical Point
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Evidence for new interference phenomena in the decay D+→K−π+μ+ν
journal, May 2002

$$\pi \pi \rightarrow K {\bar{K}}$$ π π → K K ¯ scattering up to 1.47 GeV with hyperbolic dispersion relations
journal, November 2018

Nonperturbative QCD simulations with $2 + 1$ flavors of improved staggered quarks
journal, May 2010

Data-driven dispersive analysis of the $π π$ and $π K$ scattering
journal, June 2021

Two particle states and the S -matrix elements in multi-channel scattering
journal, July 2005

Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
journal, April 2004

Light hadron masses from lattice QCD
journal, April 2012

A method to determine resonance parameters from partial-wave amplitudes
journal, September 1973

Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories
journal, September 1968

A new analysis of $\pi K$ scattering from Roy and Steiner type equations
journal, March 2004

Direct $C P$ violation in beauty and charm hadron decays
journal, September 2020

Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD
journal, January 2017

Anomalous magnetic moment of the muon in a dispersive approach
journal, December 2014

The hadronic light-by-light contribution to the muon’s anomalous magnetic moment
journal, July 2019

Analytic model of Regge trajectories
journal, April 2001

Pion–nucleon scattering in chiral perturbation theory II: Fourth order calculation
journal, August 2000

Resonances in Coupled $π K − η K$ Scattering from Quantum Chromodynamics
journal, October 2014

Resonances in coupled $π K, η K$ scattering from lattice QCD
journal, March 2015

K∗ production in K+n → KπN at 8.25 GeV/c
journal, September 1976

Scattering processes and resonances from lattice QCD
journal, April 2018

Measurements of the parameters of the $φ (1020)$ resonance through studies of the processes $e^{+} e^{-} \to K^{+} K^{-},$ $K_{S} K_{L},$ and $π^{+} π^{-} π^{0}$
journal, March 2001

A study of K∗(890) and K∗(1420) production mechanisms in K+p → K+π−Δ++ at 13 GeV/c
journal, January 1976

Compilation of coupling constants and low-energy parameters
journal, May 1983

A low lying scalar meson nonet in a unitarized meson model
journal, December 1986

Extraction of isoscalar $π π$ phase shifts from lattice QCD
journal, July 2018

The strangeness content of the nucleon from effective field theory and phenomenology
journal, March 2014

Ordinary and Extraordinary Hadrons
conference, January 2007

A partial wave analysis of the system produced in at 10 GeV/c
journal, April 1978

On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle
journal, November 2016

The K* 0(800) scalar resonance from Roy–Steiner representations of πK scattering
journal, November 2006

Brief history of the pion–nucleon sigma term
journal, June 2021

Effective-field theory analysis of the $τ^{-} \to (K π)^{-} ν_{τ}$ decays
journal, May 2019

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD
journal, July 2018

Dispersive calculation of complex Regge trajectories for the lightest $f_{2}$ resonances and the $K^{⁎} (892)$
journal, October 2015

Analysis of the pion-kaon sigma term and related topics
journal, September 2002

Amplitudes and exchange mechanisms for K∗(890) and K∗(1420) production
journal, February 1976

K π vector form factor constrained by τ → Kπντ and K l3 decays
journal, September 2010

Roy-Steiner equations for pion-nucleon scattering
journal, June 2012

Calculation of regge poles by continued fractions - I
journal, November 1962

Exact integral equation for pion-pion scattering involving only physical region partial waves
journal, September 1971