Quark-Mass Dependence of Elastic $πK$ Scattering from QCD

Wilson, David J.; Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.

doi:10.1103/PhysRevLett.123.042002

Title: Quark-Mass Dependence of Elastic $πK$ Scattering from QCD

Abstract

We present a determination of the isospin-½ elastic $πK$ scattering amplitudes in $S$ and $P$ partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the $P$-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $$κ/K_{0}^{*}$$(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

Authors:

; Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; for the Hadron Spectrum Collaboration

Publication Date:: 2019-07-24

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); Royal Society–Science Foundation Ireland University; Science and Technology Facilities Council (STFC); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF); State of Illinois

Contributing Org.:: Hadron Spectrum Collaboration

OSTI Identifier:: 1545442

Alternate Identifier(s):: OSTI ID: 1608409

Report Number(s):: JLAB-THY-19-2911; DOE/OR/23177-4665; arXiv:1904.03188
Journal ID: ISSN 0031-9007; PRLTAO; 042002

Grant/Contract Number:: AC05-06OR23177; SC0019229; SC0018416; AC05-00OR22725; AC02-05CH11231; UF160419; ST/P000681/1; OCI-0725070; ACI-1238993

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 123 Journal Issue: 4; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., and for the Hadron Spectrum Collaboration. Quark-Mass Dependence of Elastic $πK$ Scattering from QCD.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevLett.123.042002.

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                    Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., & for the Hadron Spectrum Collaboration. Quark-Mass Dependence of Elastic $πK$ Scattering from QCD.  United States.  https://doi.org/10.1103/PhysRevLett.123.042002

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                    Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., and for the Hadron Spectrum Collaboration. Wed .  
"Quark-Mass Dependence of Elastic $πK$ Scattering from QCD".  United States.  https://doi.org/10.1103/PhysRevLett.123.042002.

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@article{osti_1545442,

  title        = {Quark-Mass Dependence of Elastic $πK$ Scattering from QCD},

  author       = {Wilson, David J. and Briceño, Raúl A. and Dudek, Jozef J. and Edwards, Robert G. and Thomas, Christopher E. and for the Hadron Spectrum Collaboration},

  abstractNote = {We present a determination of the isospin-½ elastic $πK$ scattering amplitudes in $S$ and $P$ partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the $P$-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $κ/K_{0}^{*}$(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.},

  doi          = {10.1103/PhysRevLett.123.042002},

  journal      = {Physical Review Letters},

  number       = 4,

  volume       = 123,

  place        = {United States},

  year         = {2019},

  month        = {7}

}

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In this study, we determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering inmore »« less
Cited by 49
https://doi.org/10.1103/PhysRevD.92.094502

Full Text Available
Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD

Journal Article Briceño, Raul A. ; Dudek, Jozef J. ; Edwards, Robert G. ; ... - Physical Review Letters

Here, we present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. We also compute the hadronic correlation functions including all required quark propagation diagrams. From these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the S-wave phase-shift up to the Kmore »« less
Cited by 21
https://doi.org/10.1103/PhysRevLett.118.022002

Full Text Available
Decays of an exotic 1−+ hybrid meson resonance in QCD

Journal Article Woss, Antoni J. ; Dudek, Jozef J. ; Edwards, Robert G. ; ... - Physical Review D

We present the first determination of the hadronic decays of the lightest exoticmore »« less
https://doi.org/10.1103/physrevd.103.054502
Resonances in coupled πK, ηK scattering from lattice QCD

Journal Article Wilson, David J. ; Dudek, Jozef J. ; Edwards, Robert G. ; ... - Physical Review. D, Particles, Fields, Gravitation and Cosmology

Coupled-channel πK and ηK scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a qq-bar construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at mπ = 391 MeV, we find a gradual increase in the JP = 0+ πK phase-shift which may be identified with a broad scalar resonance that couples strongly to πK and weakly to ηK. The low-energy behavior of this amplitude suggests a virtual bound-state that may bemore »« less
Cited by 45
https://doi.org/10.1103/PhysRevD.91.054008

Full Text Available

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Title: Quark-Mass Dependence of Elastic $πK$ Scattering from QCD

Abstract

Citation Formats

Scalar mesons in a finite volume journal, January 2011

Helicity operators for mesons in flight on the lattice journal, January 2012

Rummukainen-Gottlieb formula on a two-particle system with different masses journal, January 2012

An improved study of the kappa resonance and the non-exotic s wave πK scatterings up to of LASS data journal, September 2006

Coupled-channel scattering on a torus journal, July 2013

Multiple-channel generalization of Lellouch-Lüscher formula journal, July 2012

Tuning for three flavors of anisotropic clover fermions with stout-link smearing journal, September 2008

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles journal, April 2017

Inverse amplitude method and Adler zeros journal, March 2008

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

Partial twisting for scalar mesons journal, January 2014

Solving lattice QCD systems of equations using mixed precision solvers on GPUs journal, September 2010

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

A method to measure the antikaon–nucleon scattering length in lattice QCD journal, November 2009

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

Moving multichannel systems in a finite volume with application to proton-proton fusion journal, November 2013

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator journal, November 2010

A study of K−π+ scattering in the reaction K−p→K−π+n at 11 GeV/c journal, January 1988

Crossing symmetry violation of unitarized ChPT amplitudes in the resonance region journal, April 2002

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

Resonance scattering phase shifts on a non-rest-frame lattice journal, September 1995

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

Unitarized chiral perturbation theory for elastic pion-pion scattering journal, January 1990

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

Utilising optimised operators and distillation to extract scattering phase shifts conference, March 2017

Relativistic, model-independent, three-particle quantization condition journal, December 2014

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

Observation of the selective coupling of K* states to the K−η channel journal, January 1988

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD journal, June 2012

Lattice study on π K scattering with moving wall source journal, April 2012

First results from 2 + 1 dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass journal, February 2009

The strange meson resonances observed in the reaction at GeV/c journal, January 1987

Toward the excited meson spectrum of dynamical QCD journal, August 2010

Two-particle multichannel systems in a finite volume with arbitrary spin journal, April 2014

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

Chiral poles and zeros and the role of the left hand cut journal, June 1997

Excited and exotic charmonium, D s and D meson spectra for two light quark masses from lattice QCD journal, December 2016

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD journal, July 2018

Three-particle systems with resonant subprocesses in a finite volume journal, January 2019

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

Multigrid solver for clover fermions conference, June 2011

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

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice journal, July 2004

Scattering lengths for two pseudoscalar meson systems journal, March 2014

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

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD journal, October 2016

There is no journal, June 2001

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

Scattering phases for meson and baryon resonances on general moving-frame lattices journal, November 2012

Hadron-Hadron interactions from N f = 2 + 1 + 1 lattice QCD: I = 3 / 2 π K scattering length journal, December 2018

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

π K scattering in full QCD with domain-wall valence quarks journal, December 2006

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

Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General Theory journal, November 1958

K π scattering for isospin 1 2 and 3 2 in lattice QCD journal, September 2012

K π scattering and the K * decay width from lattice QCD journal, September 2013

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

Scalar mesons moving in a finite volume and the role of partial wave mixing journal, August 2012

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

Scattering processes and resonances from lattice QCD journal, April 2018

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

N / D description of two meson amplitudes and chiral symmetry journal, September 1999

The κ resonance in s wave πK scatterings journal, March 2004

Inverse amplitude method in ππ scattering in chiral perturbation theory to two loops journal, January 2002

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

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

An a 0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD journal, May 2016

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

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

Lattice QCD study of the K * ( 892 ) meson decay width journal, November 2012

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

Adjoint sources in lattice gauge theory journal, September 1985

Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV journal, April 2016

Resonant π + γ → π + π 0 Amplitude from Quantum Chromodynamics journal, December 2015

π π → π γ * amplitude and the resonant ρ → π γ * transition from lattice QCD journal, June 2016

Finite-volume effects for two-hadron states in moving frames journal, October 2005

Finite volume effects in pion-kaon scattering and reconstruction of the κ(800) resonance journal, January 2012

Scalar mesons in a finite volume
journal, January 2011

Helicity operators for mesons in flight on the lattice
journal, January 2012

Rummukainen-Gottlieb formula on a two-particle system with different masses
journal, January 2012

An improved study of the kappa resonance and the non-exotic s wave πK scatterings up to of LASS data
journal, September 2006

Coupled-channel scattering on a torus
journal, July 2013

Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012

Tuning for three flavors of anisotropic clover fermions with stout-link smearing
journal, September 2008

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017

Inverse amplitude method and Adler zeros
journal, March 2008

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

Partial twisting for scalar mesons
journal, January 2014

Solving lattice QCD systems of equations using mixed precision solvers on GPUs
journal, September 2010

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

A method to measure the antikaon–nucleon scattering length in lattice QCD
journal, November 2009

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

Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
journal, November 2010

A study of K−π+ scattering in the reaction K−p→K−π+n at 11 GeV/c
journal, January 1988

Crossing symmetry violation of unitarized ChPT amplitudes in the resonance region
journal, April 2002

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

Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995

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

Unitarized chiral perturbation theory for elastic pion-pion scattering
journal, January 1990

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

Utilising optimised operators and distillation to extract scattering phase shifts
conference, March 2017

Relativistic, model-independent, three-particle quantization condition
journal, December 2014

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

Observation of the selective coupling of K* states to the K−η channel
journal, January 1988

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD
journal, June 2012

Lattice study on $π K$ scattering with moving wall source
journal, April 2012

First results from $2 + 1$ dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass
journal, February 2009

The strange meson resonances observed in the reaction at GeV/c
journal, January 1987

Toward the excited meson spectrum of dynamical QCD
journal, August 2010

Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014

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

Chiral poles and zeros and the role of the left hand cut
journal, June 1997

Excited and exotic charmonium, D s and D meson spectra for two light quark masses from lattice QCD
journal, December 2016

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018

Three-particle systems with resonant subprocesses in a finite volume
journal, January 2019

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

Multigrid solver for clover fermions
conference, June 2011

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

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004

Scattering lengths for two pseudoscalar meson systems
journal, March 2014

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

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD
journal, October 2016

There is no
journal, June 2001

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

Scattering phases for meson and baryon resonances on general moving-frame lattices
journal, November 2012

Hadron-Hadron interactions from $N_{f} = 2 + 1 + 1$ lattice QCD: $I = 3 / 2$ $π K$ scattering length
journal, December 2018

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

$π K$ scattering in full QCD with domain-wall valence quarks
journal, December 2006

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

Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General Theory
journal, November 1958

$K$ $π$ scattering for isospin $\frac{1}{2}$ and $\frac{3}{2}$ in lattice QCD
journal, September 2012

$K π$ scattering and the $K^{*}$ decay width from lattice QCD
journal, September 2013

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

Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012

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

Scattering processes and resonances from lattice QCD
journal, April 2018

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

$N / D$ description of two meson amplitudes and chiral symmetry
journal, September 1999

The κ resonance in s wave πK scatterings
journal, March 2004

Inverse amplitude method in ππ scattering in chiral perturbation theory to two loops
journal, January 2002

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

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

An $a_{0}$ resonance in strongly coupled $π η$ , $K \bar{K}$ scattering from lattice QCD
journal, May 2016

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

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

Lattice QCD study of the $K^{*} (892)$ meson decay width
journal, November 2012

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

Adjoint sources in lattice gauge theory
journal, September 1985

Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
journal, April 2016

Resonant $π^{+} γ \to π^{+} π^{0}$ Amplitude from Quantum Chromodynamics
journal, December 2015

$π π \to π γ^{}$ amplitude and the resonant $ρ \to π γ^{}$ transition from lattice QCD
journal, June 2016

Finite-volume effects for two-hadron states in moving frames
journal, October 2005

Finite volume effects in pion-kaon scattering and reconstruction of the κ(800) resonance
journal, January 2012

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector
journal, November 2011

The Chroma Software System for Lattice QCD
journal, March 2005

Study of Kπ scattering using the reactions
journal, February 1978