Cross-channel study of pion scattering from lattice QCD

Mai, M.; Culver, C.; Alexandru, A.; Döring, M.; Lee, F. X.

doi:10.1103/PhysRevD.100.114514

Title: Cross-channel study of pion scattering from lattice QCD

Abstract

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain, $$m_πa^{I=0}_0 =$$ 0.2132(9), and $$m_πa^{I=2}_0 =$$ 0.0433(2) as well as $$m_σ =$$ 443(3) – $$i$$221(6) MeV and $$m_ρ =$$ 724(4) – $$i$$67(1) MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.

Authors:

Mai, M.; Culver, C.; Alexandru, A.;

; Lee, F. X.

Publication Date:: Tue Dec 24 00:00:00 EST 2019

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)

OSTI Identifier:: 1580302

Alternate Identifier(s):: OSTI ID: 1581135

Report Number(s):: JLAB-THY-19-3017; DOE/OR/23177-4765; arXiv:1908.01847
Journal ID: ISSN 2470-0010; PRVDAQ; 114514

Grant/Contract Number:: FG02-95ER40907; AC05-06OR23177; PHY-1151648; PHY-1452055

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Mai, M., Culver, C., Alexandru, A., Döring, M., and Lee, F. X. Cross-channel study of pion scattering from lattice QCD.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.114514.

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                    Mai, M., Culver, C., Alexandru, A., Döring, M., & Lee, F. X. Cross-channel study of pion scattering from lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.100.114514

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                    Mai, M., Culver, C., Alexandru, A., Döring, M., and Lee, F. X. Tue .  
"Cross-channel study of pion scattering from lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.100.114514.

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@article{osti_1580302,

  title        = {Cross-channel study of pion scattering from lattice QCD},

  author       = {Mai, M. and Culver, C. and Alexandru, A. and Döring, M. and Lee, F. X.},

  abstractNote = {We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain, $m_πa^{I=0}_0 =$ 0.2132(9), and $m_πa^{I=2}_0 =$ 0.0433(2) as well as $m_σ =$ 443(3) – $i$221(6) MeV and $m_ρ =$ 724(4) – $i$67(1) MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.},

  doi          = {10.1103/PhysRevD.100.114514},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 100,

  place        = {United States},

  year         = {Tue Dec 24 00:00:00 EST 2019},

  month        = {Tue Dec 24 00:00:00 EST 2019}

}

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Physical Review D, Vol. 94, Issue 3
DOI: 10.1103/PhysRevD.94.034501

Isoscalar $π π, K \bar{K}, η η$ scattering and the $σ, f_{0}, f_{2}$ mesons from QCD
journal, March 2018

Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.
Physical Review D, Vol. 97, Issue 5
DOI: 10.1103/PhysRevD.97.054513

$I = 2$ pion scattering amplitude with Wilson fermions
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Gupta, Rajan; Patel, Apoorva; Sharpe, Stephen R.
Physical Review D, Vol. 48, Issue 1
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Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD
journal, February 2013

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.
Physical Review D, Vol. 87, Issue 3
DOI: 10.1103/PhysRevD.87.034505

Chiral extrapolation of the sigma resonance
journal, July 2018

Döring, Michael; Hu, Bin; Mai, Maxim
Physics Letters B, Vol. 782
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Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Lüscher, Martin
Nuclear Physics B, Vol. 354, Issue 2-3
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Inverse amplitude method in chiral perturbation theory
journal, September 1997

Dobado, A.; Peláez, J. R.
Physical Review D, Vol. 56, Issue 5
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$ρ$ meson decay in $2 + 1$ flavor lattice QCD
journal, November 2011

Aoki, S.; Ishikawa, K-I.; Ishizuka, N.
Physical Review D, Vol. 84, Issue 9
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On-shell improved lattice gauge theories
journal, September 1985

Lüscher, M.; Weisz, P.
Communications in Mathematical Physics, Vol. 98, Issue 3
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Finite volume effects in pion-kaon scattering and reconstruction of the κ(800) resonance
journal, January 2012

Döring, M.; Meißner, U. -G.
Journal of High Energy Physics, Vol. 2012, Issue 1
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Phase-shift analysis of π+π− scattering between 1.0 and 1.8 GeV based on fixed momentum transfer analyticity (II)
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Froggatt, C. D.; Petersen, J. L.
Nuclear Physics B, Vol. 129, Issue 1
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Two-Flavor Simulations of $ρ (770)$ and the Role of the $K \bar{K}$ Channel
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Hu, B.; Molina, R.; Döring, M.
Physical Review Letters, Vol. 117, Issue 12
DOI: 10.1103/PhysRevLett.117.122001

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journal, August 2016

Fu, Ziwen; Wang, Lingyun
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$I = 0$ $π π$ $s$ -wave scattering length from lattice QCD
journal, July 2018

Fu, Ziwen; Chen, Xu
Physical Review D, Vol. 98, Issue 1
DOI: 10.1103/PhysRevD.98.014514

ππ phase-shift analysis below the threshold
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Estabrooks, P.; Martin, A. D.
Nuclear Physics B, Vol. 79, Issue 2
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Extracting rho and Delta resonances from lattice simulations at small quark masses
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Schierholz, Gerrit
Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008)
DOI: 10.22323/1.066.0136

Non-perturbative improvement of nHYP smeared Wilson fermions
conference, March 2008

Hoffmann, Roland; Hasenfratz, Anna; Schaefer, Stefan
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)
DOI: 10.22323/1.042.0104

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Title: Cross-channel study of pion scattering from lattice QCD

Abstract

Citation Formats

Connecting physical resonant amplitudes and lattice QCD journal, June 2016

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states journal, June 1986

The pion vector form factor from lattice QCD and NNLO chiral perturbation theory journal, November 2013

3-body quantization condition in unitary isobar formalism conference, May 2019

Resonance parameters of the rho-meson from asymmetrical lattices journal, January 2013

Finite-Volume Spectrum of π + π + and π + π + π + Systems journal, February 2019

ππ scattering journal, June 2001

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Multi-mass solvers for lattice QCD on GPUs journal, February 2012

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Chiral Perturbation Theory and Final-State Theorem journal, November 1988

Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop journal, March 2010

Timelike pion form factor in lattice QCD journal, March 2015

Chiral perturbation theory: Expansions in the mass of the strange quark journal, January 1985

Lattice calculation of I = 2 pion scattering length journal, September 1992

Scattering phase-shift formulas for mesons and baryons in elongated boxes journal, September 2017

ρ and K * resonances on the lattice at nearly physical quark masses and N f = 2 journal, March 2016

Hypercubic smeared links for dynamical fermions journal, May 2007

P -wave π π scattering and the ρ resonance from lattice QCD journal, August 2017

I = 2 π π scattering phase shift with two flavors of O a improved dynamical quarks journal, October 2004

Chiral symmetry constraints on resonant amplitudes journal, March 2018

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD journal, February 2019

Chiral extrapolations of the ρ ( 770 ) meson in N f = 2 + 1 lattice QCD simulations journal, August 2017

Review of Particle Physics journal, August 2018

Novel quark-field creation operator construction for hadronic physics in lattice QCD journal, September 2009

Hadron-hadron interactions from N f = 2 + 1 + 1 lattice QCD: isospin-2 ππ scattering length journal, September 2015

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD journal, November 2015

Nature of the f 0 ( 600 ) Scalar Meson from its N c Dependence at Two Loops in Unitarized Chiral Perturbation Theory journal, December 2006

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

I = 2 π π scattering from fully-dynamical mixed-action lattice QCD journal, March 2006

Lattice QCD calculation of the ρ meson decay width journal, November 2007

Resonance parameters of the ρ meson from lattice QCD journal, May 2011

Experimental study of 30 000 K e 4 decays journal, February 1977

Lattice QCD calculation of full pion scattering lengths journal, October 1993

Lattice study of pion-pion scattering using Nf=2+1 Wilson improved quarks with masses down to their physical values. conference, May 2015

Lattice QCD study of the s -wave π π scattering lengths in the I = 0 and 2 channels journal, April 2013

Chiral perturbation theory to one loop journal, November 1984

Precise Determination of the f 0 ( 600 ) and f 0 ( 980 ) Pole Parameters from a Dispersive Data Analysis journal, August 2011

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation journal, July 1990

Structure of the scalar mesons f 0 (980) and a 0 (980) journal, September 1995

Meson-meson scattering within one-loop chiral perturbation theory and its unitarization journal, January 2002

Scrutinizing the η-η′ mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory journal, June 2015

Isospin-0 π π s-wave scattering length from twisted mass lattice QCD journal, September 2017

π π Partial-Wave Analysis from Reactions π + p → π + π − Δ + + and π + p → K + K − Δ + + at 7.1 GeV/ c journal, March 1973

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

${\bf I=2} \boldsymbol{\pi\pi}$ potential in the HAL QCD method with all-to-all propagators journal, August 2019

Scattering lengths for two pseudoscalar meson systems journal, March 2014

Validity of ChPT - is $M_\pi=135$ MeV small enough ? conference, May 2015

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

Precise determination of the I = 2 π π scattering length from mixed-action lattice QCD journal, January 2008

Regge analysis of the ππ scattering amplitude journal, February 2012

Quark-Mass Dependence of the ρ and σ Mesons from Dispersion Relations and Chiral Perturbation Theory journal, April 2008

Erratum: Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD [Phys. Rev. D 87 , 034505 (2013)] journal, November 2014

On-shell improved lattice gauge theories journal, March 1985

Couplings of light I=0 scalar mesons to simple operators in the complex plane journal, December 2011

Erratum: Meson-meson interactions in a nonperturbative chiral approach [Phys. Rev. D 59 , 074001 (1999)] journal, May 2007

Pion scattering poles and chiral symmetry restoration journal, October 2007

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

I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD journal, September 2016

Coupled channel analysis of the ρ meson decay in lattice QCD journal, September 2011

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

The mixing angle of the lightest scalar nonet journal, November 2003

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Meson-meson interactions in a nonperturbative chiral approach journal, February 1999

Scattering processes and resonances from lattice QCD journal, April 2018

Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results journal, December 2010

On the generalized eigenvalue method for energies and matrix elements in lattice field theory journal, April 2009

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

I = 2 ππ scattering phase shift from the HAL QCD method with the LapH smearing journal, April 2018

Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD journal, October 2019

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

Erratum: Coupled channel analysis of the ρ meson decay in lattice QCD [Phys. Rev. D 84, 054503 (2011)] journal, March 2014

I = 2 pion scattering length from two-pion wave functions journal, May 2005

Rho resonance parameters from lattice QCD journal, August 2016

Isoscalar π π , K K ¯ , η η scattering and the σ , f 0 , f 2 mesons from QCD journal, March 2018

I = 2 pion scattering amplitude with Wilson fermions journal, July 1993

Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD journal, February 2013

Connecting physical resonant amplitudes and lattice QCD
journal, June 2016

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

The pion vector form factor from lattice QCD and NNLO chiral perturbation theory
journal, November 2013

3-body quantization condition in unitary isobar formalism
conference, May 2019

Resonance parameters of the rho-meson from asymmetrical lattices
journal, January 2013

Finite-Volume Spectrum of $π^{+} π^{+}$ and $π^{+} π^{+} π^{+}$ Systems
journal, February 2019

ππ scattering
journal, June 2001

Inverse amplitude method and Adler zeros
journal, March 2008

Multi-mass solvers for lattice QCD on GPUs
journal, February 2012

$S$ - and $D$ -wave phase shifts in isospin-2 $π π$ scattering from lattice QCD
journal, August 2012

Chiral Perturbation Theory and Final-State Theorem
journal, November 1988

Strange and nonstrange quark mass dependence of elastic light resonances from SU(3) unitarized chiral perturbation theory to one loop
journal, March 2010

Timelike pion form factor in lattice QCD
journal, March 2015

Chiral perturbation theory: Expansions in the mass of the strange quark
journal, January 1985

Lattice calculation of I = 2 pion scattering length
journal, September 1992

Scattering phase-shift formulas for mesons and baryons in elongated boxes
journal, September 2017

$ρ$ and $K^{*}$ resonances on the lattice at nearly physical quark masses and $N_{f} = 2$
journal, March 2016

Hypercubic smeared links for dynamical fermions
journal, May 2007

$P$ -wave $π π$ scattering and the $ρ$ resonance from lattice QCD
journal, August 2017

$I = 2 π π$ scattering phase shift with two flavors of $O (a)$ improved dynamical quarks
journal, October 2004

Chiral symmetry constraints on resonant amplitudes
journal, March 2018

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD
journal, February 2019

Chiral extrapolations of the $ρ (770)$ meson in $N_{f} = 2 + 1$ lattice QCD simulations
journal, August 2017

Review of Particle Physics
journal, August 2018

Novel quark-field creation operator construction for hadronic physics in lattice QCD
journal, September 2009

Hadron-hadron interactions from N f = 2 + 1 + 1 lattice QCD: isospin-2 ππ scattering length
journal, September 2015

Coupled $π π$ , $K \bar{K}$ scattering in $P$ -wave and the $ρ$ resonance from lattice QCD
journal, November 2015

Nature of the $f_{0} (600)$ Scalar Meson from its $N_{c}$ Dependence at Two Loops in Unitarized Chiral Perturbation Theory
journal, December 2006

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

$I = 2$ $π π$ scattering from fully-dynamical mixed-action lattice QCD
journal, March 2006

Lattice QCD calculation of the $ρ$ meson decay width
journal, November 2007

Resonance parameters of the $ρ$ meson from lattice QCD
journal, May 2011

Experimental study of 30 000 $K_{e 4}$ decays
journal, February 1977

Lattice QCD calculation of full pion scattering lengths
journal, October 1993

Lattice study of pion-pion scattering using Nf=2+1 Wilson improved quarks with masses down to their physical values.
conference, May 2015

Lattice QCD study of the $s$ -wave $π π$ scattering lengths in the $I = 0$ and 2 channels
journal, April 2013

Chiral perturbation theory to one loop
journal, November 1984

Precise Determination of the $f_{0} (600)$ and $f_{0} (980)$ Pole Parameters from a Dispersive Data Analysis
journal, August 2011

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
journal, July 1990

Structure of the scalar mesons $f_{0}$ (980) and $a_{0}$ (980)
journal, September 1995

Meson-meson scattering within one-loop chiral perturbation theory and its unitarization
journal, January 2002

Scrutinizing the η-η′ mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory
journal, June 2015

Isospin-0 $π π$ s-wave scattering length from twisted mass lattice QCD
journal, September 2017

$π π$ Partial-Wave Analysis from Reactions $π^{+} p \to π^{+} π^{-} Δ^{+ +}$ and $π^{+} p \to K^{+} K^{-} Δ^{+ +}$ at 7.1 GeV/ c
journal, March 1973

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

${\bf I=2} \boldsymbol{\pi\pi}$ potential in the HAL QCD method with all-to-all propagators
journal, August 2019

Scattering lengths for two pseudoscalar meson systems
journal, March 2014

Validity of ChPT - is $M_\pi=135$ MeV small enough ?
conference, May 2015

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

Precise determination of the $I = 2$ $π π$ scattering length from mixed-action lattice QCD
journal, January 2008

Regge analysis of the ππ scattering amplitude
journal, February 2012

Quark-Mass Dependence of the $ρ$ and $σ$ Mesons from Dispersion Relations and Chiral Perturbation Theory
journal, April 2008

Erratum: Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD [Phys. Rev. D 87 , 034505 (2013)]
journal, November 2014

On-shell improved lattice gauge theories
journal, March 1985

Couplings of light I=0 scalar mesons to simple operators in the complex plane
journal, December 2011

Erratum: Meson-meson interactions in a nonperturbative chiral approach [Phys. Rev. D 59 , 074001 (1999)]
journal, May 2007

Pion scattering poles and chiral symmetry restoration
journal, October 2007

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

I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD
journal, September 2016

Coupled channel analysis of the $ρ$ meson decay in lattice QCD
journal, September 2011

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

The mixing angle of the lightest scalar nonet
journal, November 2003

Pion scattering in the isospin $I = 2$ channel from elongated lattices
journal, August 2019

Meson-meson interactions in a nonperturbative chiral approach
journal, February 1999

Scattering processes and resonances from lattice QCD
journal, April 2018

Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results
journal, December 2010

On the generalized eigenvalue method for energies and matrix elements in lattice field theory
journal, April 2009

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

I = 2 ππ scattering phase shift from the HAL QCD method with the LapH smearing
journal, April 2018

Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD
journal, October 2019

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

Erratum: Coupled channel analysis of the $ρ$ meson decay in lattice QCD [Phys. Rev. D 84, 054503 (2011)]
journal, March 2014

$I = 2$ pion scattering length from two-pion wave functions
journal, May 2005

Rho resonance parameters from lattice QCD
journal, August 2016

Isoscalar $π π, K \bar{K}, η η$ scattering and the $σ, f_{0}, f_{2}$ mesons from QCD
journal, March 2018

$I = 2$ pion scattering amplitude with Wilson fermions
journal, July 1993

Energy dependence of the $ρ$ resonance in $π π$ elastic scattering from lattice QCD
journal, February 2013

Chiral extrapolation of the sigma resonance
journal, July 2018

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Inverse amplitude method in chiral perturbation theory
journal, September 1997