skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Comprehensive amplitude analysis of γ γ π + π - , π 0 π 0 and K ¯ K below 1.5 GeV

Abstract

In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the γγ to meson pair amplitudes as possible. Having data with limited angular coverage, typically |cosθ| < 0.6-0.8, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing-symmetry makes up for the experimentally missing information. Above 1.5 GeV multi-meson production channels become important and we have too little information to resolve the amplitudes. Nevertheless, below 1.5 GeV the two photon production of hadron pairs serves as a paradigm for the application of S-matrix techniques. Final state interactions among the meson pairs is critical to this analysis. To fix these, we include the latest ππ → ππ, K⁻K scattering amplitudes given by dispersive analyses, supplemented in the K⁻K threshold regionmore » by the recent precision Dalitz plot analysis from BaBar. With these hadronic amplitudes built into unitarity, we can constrain the overall description of γγ → ππ and K⁻K datasets, both integrated and differential cross-sections, including the high statistics charged and neutral pion data from Belle. A region of solutions is found for the γγ → ππ partial waves with both isospin 0 and 2. Since this analysis invokes coupled hadronic channels, even the relatively poor integrated cross-section data on γγ → K⁻K narrows the patch of solutions to essentially a single form. For this we present the complete partial wave amplitudes, show how well they fit all the available data, and give the two photon couplings of scalar and tensor resonances that appear.« less

Authors:
 [1];  [1]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1156888
Report Number(s):
JLAB-THY-14-1842; DOE/OR/23177-3003; arXiv:1404.7524
Journal ID: ISSN 1550-7998; PRVDAQ; TRN: US1600832
Grant/Contract Number:  
AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. D, Particles, Fields, Gravitation and Cosmology
Additional Journal Information:
Journal Volume: 90; Journal Issue: 3; Journal ID: ISSN 1550-7998
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Dai, Ling-Yun, and Pennington, Michael R. Comprehensive amplitude analysis of γγ→π+π-,π0π0 and K¯K below 1.5 GeV. United States: N. p., 2014. Web. doi:10.1103/PhysRevD.90.036004.
Dai, Ling-Yun, & Pennington, Michael R. Comprehensive amplitude analysis of γγ→π+π-,π0π0 and K¯K below 1.5 GeV. United States. https://doi.org/10.1103/PhysRevD.90.036004
Dai, Ling-Yun, and Pennington, Michael R. 2014. "Comprehensive amplitude analysis of γγ→π+π-,π0π0 and K¯K below 1.5 GeV". United States. https://doi.org/10.1103/PhysRevD.90.036004. https://www.osti.gov/servlets/purl/1156888.
@article{osti_1156888,
title = {Comprehensive amplitude analysis of γγ→π+π-,π0π0 and K¯K below 1.5 GeV},
author = {Dai, Ling-Yun and Pennington, Michael R.},
abstractNote = {In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the γγ to meson pair amplitudes as possible. Having data with limited angular coverage, typically |cosθ| < 0.6-0.8, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing-symmetry makes up for the experimentally missing information. Above 1.5 GeV multi-meson production channels become important and we have too little information to resolve the amplitudes. Nevertheless, below 1.5 GeV the two photon production of hadron pairs serves as a paradigm for the application of S-matrix techniques. Final state interactions among the meson pairs is critical to this analysis. To fix these, we include the latest ππ → ππ, K⁻K scattering amplitudes given by dispersive analyses, supplemented in the K⁻K threshold region by the recent precision Dalitz plot analysis from BaBar. With these hadronic amplitudes built into unitarity, we can constrain the overall description of γγ → ππ and K⁻K datasets, both integrated and differential cross-sections, including the high statistics charged and neutral pion data from Belle. A region of solutions is found for the γγ → ππ partial waves with both isospin 0 and 2. Since this analysis invokes coupled hadronic channels, even the relatively poor integrated cross-section data on γγ → K⁻K narrows the patch of solutions to essentially a single form. For this we present the complete partial wave amplitudes, show how well they fit all the available data, and give the two photon couplings of scalar and tensor resonances that appear.},
doi = {10.1103/PhysRevD.90.036004},
url = {https://www.osti.gov/biblio/1156888}, journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
issn = {1550-7998},
number = 3,
volume = 90,
place = {United States},
year = {Fri Aug 15 00:00:00 EDT 2014},
month = {Fri Aug 15 00:00:00 EDT 2014}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 74 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Two-photon production of pion pairs
journal, September 1990


An experimental study of the processγγ→π + π −
journal, September 1992


Measurement of π 0 π 0 production in two-photon collisions
journal, June 1990


Meson pair production in γγ scattering and implications for scalar mesons
journal, September 1983


Low energy γγ→ππ cross section and the qed born amplitude
journal, June 1987


Is low energy γγ→π0π0 predictable?
journal, November 1991


What we can learn from γγ→ππ,K $$\bar K$$ in the resonance region
journal, September 1988


Amplitude analysis ofγγ→ππ from threshold to 1.4 GeV
journal, December 1990


Determination of radiative widths of scalar mesons from experimental results on $\gamma\gamma\to\pi\pi$
journal, June 1999


High statistics study of the f 0 ( 980 ) resonance in γ γ π + π production
journal, March 2007


High Statistics Measurement of the Cross Sections of γγ→π + π - Production
journal, July 2007


High-statistics study of neutral-pion pair production in two-photon collisions
journal, March 2009


High-statistics study of KFormula pair production in two-photon collisions
journal, December 2013


Physics with the KLOE-2 experiment at the upgraded DAΦNE
journal, June 2010


Amplitude analysis of high statistics results on γγ→π+π- and the two photon width of isoscalar states
journal, June 2008


Sigma Coupling to Photons: Hidden Scalar in γ γ π 0 π 0
journal, July 2006


ππ Phase-shift analysis from 600 to 1900 MeV
journal, November 1973


Amplitude analysis of the K S 0 K S 0 system produced in the reaction π p K S 0 K S 0 n at 23 GeV/ c
journal, April 1982


Search for direct CP violating charge asymmetries in K±→π±π+π- and K±→π±π0π0 decays
journal, November 2007


New high statistics measurement of Ke4 decay form factors and ππ scattering phase shifts
journal, February 2008


Precise tests of low energy QCD from $\mbox {$\mathrm {K}_{\mathrm {e}4}$}$ decay properties
journal, November 2010


Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
journal, April 2011


Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations
journal, March 2008


Pion-pion scattering amplitude. II. Improved analysis above K ¯ K threshold
journal, July 2006


Erratum: Pion-pion scattering amplitude. II. Improved analysis above K ¯ K threshold [Phys. Rev. D 74 , 014001 (2006)]
journal, October 2006


Pion-pion scattering amplitude
journal, April 2005


Measurement ofK + K − production in γγ collisions
journal, June 1990


Production of in photon-photon collisions and the excitation of the tensor meson f′(1515)
journal, January 1983


Pion and Kaon Pair Production in Photon-Photon Collisions
journal, July 1986


TheK S 0 K S 0 final state in γγ interactions
journal, March 1989


Search for two-photon production of resonances decaying intoK $$\bar K$$ andK $$\bar K$$ ?
journal, June 1985


Lightest scalar and tensor resonances in γ γ π π after the Belle experiment
journal, April 2008


Lightest scalar resonances and the dynamics of the γγ → ππ reactions
journal, November 2008


Light scalar mesons in photon–photon collisions
journal, August 2011


Phenomenological σ models
journal, June 1994


Lightest Scalar in the S U L ( 2 ) × S U R ( 2 ) Linear σ Model
journal, August 2007


The axial vector current in beta decay
journal, May 1960


Theoretical study of the γγ → meson-meson reaction
journal, February 1998


σ and <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>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> substructures 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:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>, <mml:math altimg="si3.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:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:mo>,</mml:mo><mml:mi>ϕ</mml:mi></mml:math> radiative and <mml:math altimg="si4.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>D</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> semi-leptonic decays
journal, January 2011


MO analysis of the high statistics Belle results on γ γ→π + π −, π 0 π 0 with chiral constraints
journal, October 2010


Roy–Steiner equations for γγ→ππ
journal, September 2011


Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
journal, April 2013


Review of Particle Physics
journal, July 2012


Observation of a Narrow Charmoniumlike State in Exclusive B ± K ± π + π J / ψ Decays
journal, December 2003


Observation of a Broad Structure in the π + π J / ψ Mass Spectrum around 4.26 GeV / c 2
journal, September 2005


Meson dynamics beyond the quark model: Study of final-state interactions
journal, March 1987


New data on the K K ¯ threshold region and the nature of the f 0 ( S * )
journal, August 1993


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


Two-pion production in photon-photon collisions
journal, January 1988


The reaction γγ→ π 0 π 0 and chiral loops
journal, May 1988


Low-energy photon-photon collisions to two-loop order
journal, July 1994


Dalitz plot analysis of D s + π + π π +
journal, February 2009


Dalitz plot analysis of D s + K + K π +
journal, March 2011


Left-hand singularities, hadron form factors and the properties of the σ meson
journal, December 2001


ππ scattering
journal, June 2001


Mass and Width of the Lowest Resonance in QCD
journal, April 2006


The pole structure of the unitary, crossing symmetric low energy ππ scattering amplitudes
journal, February 2005


Pole Analysis on Unitarized SU(3) × SU(3) One Loop χPT Amplitudes
journal, May 2012


Pole Analysis of Unitarized One Loop χ PT Amplitudes—A Triple Channel Study
journal, September 2012


Scalar meson and glueball decays within a effective chiral approach
journal, September 2005


Two-gluon jets from υ'(10.0)
journal, January 1978


Exclusive Hadron Production in Two-Photon Reactions
journal, October 1986


Relativistic effects in γ γ decays of P -wave positronium and q q ¯ systems
journal, April 1991


Radiative transitions of low-lying positive-parity mesons
journal, September 1976


Two-photon decay width of the sigma meson
journal, February 2008


Two-photon decay of a light scalar quark-antiquark state
conference, January 2008

  • Giacosa, Francesco; Rupp, George; van Beveren, Eef
  • SCADRON70: Workshop on Scalar Mesons and Related Topics Honoring Michael Scadron's 70th Birthday, AIP Conference Proceedings
  • https://doi.org/10.1063/1.2973491

To search for four-quark states in γγ-collisions
journal, March 1982


K K ¯ molecules
journal, April 1990


Do Multiquark Hadrons Exist?
journal, March 1982


Two-photon decays of hadronic molecules
journal, April 2007


QCD tests of the puzzling scalar mesons
journal, June 2006


Masses, decays and mixings of gluonia in QCD
journal, January 1998


Glueball nature of 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:mi>σ</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>600</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> from ππ and γγ scatterings
journal, July 2008


Two-photon width and gluonic component of
journal, September 2008


Improved dispersion relations for <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:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mo>→</mml:mo><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>
journal, January 2008


Two photons into π0π0
journal, June 2008


Light O[sup ++] Mesons: Scalargators in Florida
conference, January 2010

  • Pennington, M. R.; Crede, Volker; Eugenio, Paul
  • HADRON 2009: Proceedings of the XIII International Conference on Hadron Spectroscopy, AIP Conference Proceedings
  • https://doi.org/10.1063/1.3483333

Pole counting and resonance classification
journal, July 1992


Sum Rules for Light-by-Light Scattering
journal, November 2010


Light-by-light scattering sum rules constraining meson transition form factors
journal, June 2012


Status of hadronic light-by-light scattering in the muong−2
journal, June 2014


Multiquark hadrons. I. Phenomenology of Q 2 Q ¯ 2 mesons
journal, January 1977


Exotica
journal, March 2005


Putative light scalar nonet
journal, March 1999


New Look at Scalar Mesons
journal, November 2004


Positive parity scalar mesons in the 1–2 GeV mass range
journal, February 2007


A theory of scalar mesons
journal, May 2008


Tetraquark Mesons in Large- N Quantum Chromodynamics
journal, June 2013


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


Chiral perturbation theory, the 1 / N c expansion and Regge behavior determine the structure of the lightest scalar meson
journal, November 2011


Two-photon physics at KLOE/KLOE-2
journal, April 2012


Review of Particle Physics
text, January 2008


Low-energy photon-photon collisions to two-loop order
book, January 2005


Theoretical study of the γγ→meson-meson reaction
conference, January 1998


What we can learn from ?????,K $$\bar K$$ in the resonance region
journal, December 1988


Mechanism for a next-to-lowest lying scalar meson nonet
conference, January 2000


Review of Particle Physics
text, January 2018


Dalitz plot analysis of Ds+→K+K-π+
text, January 2011


Review of Particle Physics
text, January 2012


A low-lying scalar meson nonet in a unitarized meson model
text, January 2007


A Theory of Scalar Mesons
text, January 2008


Sum rules for light-by-light scattering
text, January 2010


Mass and width of the lowest resonance in QCD
text, January 2005


Putative Light Scalar Nonet
text, January 1998


Works referencing / citing this record:

Muon g – 2 theory: The hadronic part
journal, January 2018


Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules
journal, October 2018


Nature of the Y ( 4260 ) : A light-quark perspective
journal, April 2019


Lattice QCD Calculation of Hadronic Light-by-Light Scattering
journal, November 2015


Dispersion relation for hadronic light-by-light scattering: two-pion contributions
text, January 2017


Theoretical analysis of the γγ (*)π 0 η process
journal, January 2019


Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules
text, January 2018


Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules
text, January 2017


Light-by-light scattering sum rules in light of new data
text, January 2016


Dispersion relation for hadronic light-by-light scattering: two-pion contributions
text, January 2017