Chiral symmetry and π-π scattering in the Covariant Spectator Theory

Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz

doi:10.1103/PhysRevD.90.096008

Title: Chiral symmetry and $π$ - $π$ scattering in the Covariant Spectator Theory

Abstract

The π-π scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similarly to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward Takahashi identity to the CST π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. Thus, the Adler self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.

Authors:

Biernat, Elmar P. ^[1]; Peña, M. T. ^[1]; Ribeiro, J. E. ^[1]; Stadler, Alfred ^[2]; Gross, Franz ^[3]

Univ. de Lisboa, Lisboa (Portugal)
Univ. de Lisboa, Lisboa (Portugal); Univ. de Evora, Evora (Portugal)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Fri Nov 14 00:00:00 EST 2014

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:: 1163888

Report Number(s):: JLAB-THY-14-1933; arXiv:1408.1625; DOE/OR/23177-3151
Journal ID: ISSN 1550-7998; PRVDAQ; ArticleNumber: 096008; TRN: US1600833

Grant/Contract Number:: AC05-06OR23177; PTDC/FIS/113940/2009; CFTP-FCT; 283286

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. D, Particles, Fields, Gravitation and Cosmology

Additional Journal Information:: Journal Volume: 90; Journal Issue: 9; 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


                    Biernat, Elmar P., Peña, M. T., Ribeiro, J. E., Stadler, Alfred, and Gross, Franz. Chiral symmetry and π-π scattering in the Covariant Spectator Theory.  United States: N. p., 2014. 
Web.  doi:10.1103/PhysRevD.90.096008.

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                    Biernat, Elmar P., Peña, M. T., Ribeiro, J. E., Stadler, Alfred, & Gross, Franz. Chiral symmetry and π-π scattering in the Covariant Spectator Theory.  United States.  https://doi.org/10.1103/PhysRevD.90.096008

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                    Biernat, Elmar P., Peña, M. T., Ribeiro, J. E., Stadler, Alfred, and Gross, Franz. Fri .  
"Chiral symmetry and π-π scattering in the Covariant Spectator Theory".  United States.  https://doi.org/10.1103/PhysRevD.90.096008.  https://www.osti.gov/servlets/purl/1163888.

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@article{osti_1163888,

  title        = {Chiral symmetry and π-π scattering in the Covariant Spectator Theory},

  author       = {Biernat, Elmar P. and Peña, M. T. and Ribeiro, J. E. and Stadler, Alfred and Gross, Franz},

  abstractNote = {The π-π scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similarly to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward Takahashi identity to the CST π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. Thus, the Adler self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.},

  doi          = {10.1103/PhysRevD.90.096008},

  journal      = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

  number       = 9,

  volume       = 90,

  place        = {United States},

  year         = {Fri Nov 14 00:00:00 EST 2014},

  month        = {Fri Nov 14 00:00:00 EST 2014}

}

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Works referenced in this record:

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Works referencing / citing this record:

Heavy and Heavy-Light Mesons in the Covariant Spectator Theory
journal, March 2018

Stadler, Alfred; Leitão, Sofia; Peña, M. T.
Few-Body Systems, Vol. 59, Issue 3
DOI: 10.1007/s00601-018-1355-1

Quark Mass Functions and Pion Structure in the Covariant Spectator Theory
journal, May 2018

Biernat, Elmar P.; Gross, Franz; Peña, Teresa
Few-Body Systems, Vol. 59, Issue 5
DOI: 10.1007/s00601-018-1401-z

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
journal, December 2018

Biernat, Elmar P.; Gross, Franz; Peña, M. T.
Physical Review D, Vol. 98, Issue 11
DOI: 10.1103/physrevd.98.114033

Aspects of open-flavour mesons in a comprehensive DSBSE study
journal, October 2017

Hilger, T.; Gómez-Rocha, M.; Krassnigg, A.
The European Physical Journal A, Vol. 53, Issue 10
DOI: 10.1140/epja/i2017-12384-4

Comparison of two Minkowski-space approaches to heavy quarkonia
journal, October 2017

Leitão, Sofia; Li, Yang; Maris, Pieter
The European Physical Journal C, Vol. 77, Issue 10
DOI: 10.1140/epjc/s10052-017-5248-0

Comparison of two Minkowski-space approaches to heavy quarkonia
text, January 2017

Leitão, Sofia; Li, Yang; Maris, Pieter
arXiv
DOI: 10.48550/arxiv.1705.06178

Quark mass functions and pion structure in the Covariant Spectator Theory
text, January 2018

Biernat, E. P.; Gross, F.; Peña, M. T.
arXiv
DOI: 10.48550/arxiv.1802.00266

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Title: Chiral symmetry and π - π scattering in the Covariant Spectator Theory

Abstract

Citation Formats

Mesons in a relativized quark model with chromodynamics journal, July 1985

Spectrum of Charmed Quark-Antiquark Bound States journal, February 1975

Charmonium: The model journal, June 1978

The heavy quark potential and the ϒ, J/ψ systems journal, March 1979

Flavor structure of the excited baryon spectra from lattice QCD journal, March 2013

Coupled-channel scattering on a torus journal, July 2013

Quantum chromodynamics and other field theories on the light cone journal, August 1998

Explicitly covariant light-front dynamics and relativistic few-body systems journal, July 1998

Light-front Bethe-Salpeter equation journal, March 2000

Poincaré- and gauge-invariant two-dimensional quantum chromodynamics journal, January 1978

Instability of the Chiral-Invariant Vacuum for a Confining Potential journal, January 1983

Chiral non-invariant solutions of the gap equation for a confining potential journal, January 1984

Current-quark model in a P 0 3 condensed vacuum journal, September 1990

π, K , ρ, φ as qq¯ bound states of the Salpeter equation in a 3 P 0 condensed vacuum journal, September 1990

Generalized resonating-group-method equations in a P 0 3 q q ¯ condensed vacuum. The φ and ρ resonances journal, September 1990

Mesonic states and vacuum replicas in potential quark models for QCD journal, November 2004

The infrared behaviour of QCD Green's functions Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states journal, November 2001

Dyson–Schwinger Equations: A Tool for Hadron Physics journal, June 2003

Infrared properties of QCD from Dyson–Schwinger equations journal, June 2006

On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations journal, October 2013

Pion electromagnetic form factor in the covariant spectator theory journal, January 2014

Decoupling confinement and chiral-symmetry breaking: An explicit model journal, February 1992

Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current journal, February 1965

Quark-antiquark bound states in the relativistic spectator formalism journal, February 2001

Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space journal, January 2014

A Relativistic Equation for Bound-State Problems journal, December 1951

Three-Dimensional Covariant Integral Equations for Low-Energy Systems journal, October 1969

Covariant, chirally symmetric, confining model of mesons journal, April 1991

Axial-Vector Vertex in Spinor Electrodynamics journal, January 1969

Analytic proof that the quark model complies with partially conserved axial current theorems journal, March 2003

Chirally symmetric quark description of low energy π − π scattering journal, April 2002

Current conservation and interaction currents in relativistic meson theories journal, November 1987

Unitary, relativistic resonance model for π N scattering journal, February 1993

Unitary, gauge invariant, relativistic resonance model for pion photoproduction journal, May 1996

Chiral symmetry breaking in Coulomb gauge QCD journal, October 1984

π - and K -meson Bethe-Salpeter amplitudes journal, December 1997

Chiral symmetry and spin dependence of the quark-antiquark forces in quarkonium journal, February 1993

Effects of nonperturbatively improved dynamical fermions in QCD at fixed lattice spacing journal, January 2002

New perspective on the scalar meson puzzle, from spontaneous chiral symmetry breaking beyond BCS journal, August 1999

Pion Scattering Lengths journal, September 1966

JaxoDraw: A graphical user interface for drawing Feynman diagrams journal, August 2004

Heavy and Heavy-Light Mesons in the Covariant Spectator Theory journal, March 2018

Quark Mass Functions and Pion Structure in the Covariant Spectator Theory journal, May 2018

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space journal, December 2018

Aspects of open-flavour mesons in a comprehensive DSBSE study journal, October 2017

Comparison of two Minkowski-space approaches to heavy quarkonia journal, October 2017

Comparison of two Minkowski-space approaches to heavy quarkonia text, January 2017

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Title: Chiral symmetry and $π$ - $π$ scattering in the Covariant Spectator Theory

Mesons in a relativized quark model with chromodynamics
journal, July 1985

Spectrum of Charmed Quark-Antiquark Bound States
journal, February 1975

Charmonium: The model
journal, June 1978

The heavy quark potential and the ϒ, J/ψ systems
journal, March 1979

Flavor structure of the excited baryon spectra from lattice QCD
journal, March 2013

Coupled-channel scattering on a torus
journal, July 2013

Quantum chromodynamics and other field theories on the light cone
journal, August 1998

Explicitly covariant light-front dynamics and relativistic few-body systems
journal, July 1998

Light-front Bethe-Salpeter equation
journal, March 2000

Poincaré- and gauge-invariant two-dimensional quantum chromodynamics
journal, January 1978

Instability of the Chiral-Invariant Vacuum for a Confining Potential
journal, January 1983

Chiral non-invariant solutions of the gap equation for a confining potential
journal, January 1984

Current-quark model in a ${}^{3}P_{0}$ condensed vacuum
journal, September 1990

π, K , ρ, φ as qq¯ bound states of the Salpeter equation in a ${}^{3}$ $P_{0}$ condensed vacuum
journal, September 1990

Generalized resonating-group-method equations in a ${}^{3}P_{0}$ $q \bar{q}$ condensed vacuum. The $φ$ and $ρ$ resonances
journal, September 1990

Mesonic states and vacuum replicas in potential quark models for QCD
journal, November 2004

The infrared behaviour of QCD Green's functions Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states
journal, November 2001

Dyson–Schwinger Equations: A Tool for Hadron Physics
journal, June 2003

Infrared properties of QCD from Dyson–Schwinger equations
journal, June 2006

On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations
journal, October 2013

Pion electromagnetic form factor in the covariant spectator theory
journal, January 2014

Decoupling confinement and chiral-symmetry breaking: An explicit model
journal, February 1992

Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current
journal, February 1965

Quark-antiquark bound states in the relativistic spectator formalism
journal, February 2001

Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space
journal, January 2014

A Relativistic Equation for Bound-State Problems
journal, December 1951

Three-Dimensional Covariant Integral Equations for Low-Energy Systems
journal, October 1969

Covariant, chirally symmetric, confining model of mesons
journal, April 1991

Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969

Analytic proof that the quark model complies with partially conserved axial current theorems
journal, March 2003

Chirally symmetric quark description of low energy $π - π$ scattering
journal, April 2002

Current conservation and interaction currents in relativistic meson theories
journal, November 1987

Unitary, relativistic resonance model for π N scattering
journal, February 1993

Unitary, gauge invariant, relativistic resonance model for pion photoproduction
journal, May 1996

Chiral symmetry breaking in Coulomb gauge QCD
journal, October 1984

$π$ - and $K$ -meson Bethe-Salpeter amplitudes
journal, December 1997

Chiral symmetry and spin dependence of the quark-antiquark forces in quarkonium
journal, February 1993

Effects of nonperturbatively improved dynamical fermions in QCD at fixed lattice spacing
journal, January 2002

New perspective on the scalar meson puzzle, from spontaneous chiral symmetry breaking beyond BCS
journal, August 1999

Pion Scattering Lengths
journal, September 1966

JaxoDraw: A graphical user interface for drawing Feynman diagrams
journal, August 2004

Heavy and Heavy-Light Mesons in the Covariant Spectator Theory
journal, March 2018

Quark Mass Functions and Pion Structure in the Covariant Spectator Theory
journal, May 2018

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
journal, December 2018

Aspects of open-flavour mesons in a comprehensive DSBSE study
journal, October 2017

Comparison of two Minkowski-space approaches to heavy quarkonia
journal, October 2017

Comparison of two Minkowski-space approaches to heavy quarkonia
text, January 2017

Quark mass functions and pion structure in the Covariant Spectator Theory
text, January 2018