Form factors of two-hadron states from a covariant finite-volume formalism

Baroni, Alessandro; Briceño, Raúl A.; Hansen, Maxwell T.; Ortega-Gama, Felipe G.

doi:10.1103/PhysRevD.100.034511

Title: Form factors of two-hadron states from a covariant finite-volume formalism

Abstract

Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $$\textbf 2 + \mathcal J \to \textbf 2$$ transition amplitudes. Furthermore, we give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $$\mathcal J$$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $$G$$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $$\pi \pi + \mathcal J \to \pi \pi$$ amplitude in the $$\rho$$ channel, for which the single-pion form factor, $$F_\pi(Q^2)$$, as well as the scattering phase, $$\delta_{\pi\pi}$$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

Authors:: Baroni, Alessandro; Briceño, Raúl A.; Hansen, Maxwell T.; Ortega-Gama, Felipe G.

Publication Date:: Thu Aug 01 00:00:00 EDT 2019

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:: 1557352

Alternate Identifier(s):: OSTI ID: 1557629

Report Number(s):: JLAB-THY-18-2878; DOE/OR/-23177-4598; arXiv:1812.10504
Journal ID: ISSN 2470-0010; PRVDAQ; 034511

Grant/Contract Number:: AC05-06OR23177; SC0019229; SC0010300

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.034511.

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                    Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., & Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism.  United States.  https://doi.org/10.1103/PhysRevD.100.034511

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                    Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Thu .  
"Form factors of two-hadron states from a covariant finite-volume formalism".  United States.  https://doi.org/10.1103/PhysRevD.100.034511.

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@article{osti_1557352,

  title        = {Form factors of two-hadron states from a covariant finite-volume formalism},

  author       = {Baroni, Alessandro and Briceño, Raúl A. and Hansen, Maxwell T. and Ortega-Gama, Felipe G.},

  abstractNote = {Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\textbf 2 + \mathcal J \to \textbf 2$ transition amplitudes. Furthermore, we give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $\mathcal J$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $\pi \pi + \mathcal J \to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_\pi(Q^2)$, as well as the scattering phase, $\delta_{\pi\pi}$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.},

  doi          = {10.1103/PhysRevD.100.034511},

  journal      = {Physical Review. D.},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {Thu Aug 01 00:00:00 EDT 2019},

  month        = {Thu Aug 01 00:00:00 EDT 2019}

}

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Journal Article Briceño, Raúl A. ; Jackura, Andrew W. ; Ortega-Gama, Felipe G. ; ... - Physical Review D

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https://doi.org/10.1103/PhysRevD.103.114512
Prospects for $γ^{⋆} γ^{⋆} \to π π$ via lattice QCD

Journal Article Briceño, Raúl A. ; Jackura, Andrew W. ; Rodas, Arkaitz ; ... - Physical Review. D.

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https://doi.org/10.1103/PhysRevD.107.034504

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Title: Form factors of two-hadron states from a covariant finite-volume formalism

Abstract

Citation Formats

Scalar mesons in a finite volume journal, January 2011

Emerging Understanding of the Δ I = 1 / 2 Rule from Lattice QCD journal, April 2013

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

Generalized Lüscher formula in multichannel baryon-meson scattering journal, January 2013

On analytic properties of vertex parts in quantum field theory journal, October 1959

Singularities in the physical region journal, July 1965

Coupled-channel scattering on a torus journal, July 2013

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

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

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

Discussion on triangle singularities in the Λ b → J / ψ K − p reaction journal, October 2016

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

K to π π decay amplitudes from lattice QCD journal, December 2011

Timelike pion form factor in lattice QCD journal, March 2015

Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics journal, August 2017

Double- β decay matrix elements from lattice quantum chromodynamics journal, September 2017

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions journal, May 2001

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data journal, October 2017

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

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume journal, July 2016

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

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

π γ → π π transition and the ρ radiative decay width from lattice QCD journal, October 2018

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

Three-particle scattering amplitudes from a finite volume formalism journal, May 2013

Heavy Physics Contributions to Neutrinoless Double Beta Decay from QCD journal, October 2018

Parton Physics on a Euclidean Lattice journal, June 2013

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

Lattice QCD and the Timelike Pion Form Factor journal, August 2011

Heavy-quark QCD exotica journal, March 2017

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

Two-baryon systems with twisted boundary conditions journal, April 2014

Multichannel 1 → 2 transition amplitudes in a finite volume journal, February 2015

K → ( π π ) I = 2 Decay Amplitude from Lattice QCD journal, April 2012

Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume journal, October 2015

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

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

Standard Model Prediction for Direct C P Violation in K → π π Decay journal, November 2015

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

Nuclear gluonometry journal, June 1989

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

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

Hadronic molecules journal, February 2018

Matrix elements of unstable states journal, September 2012

Off-forward gluonic structure of vector mesons journal, June 2017

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

Three-body unitarity in the finite volume journal, December 2017

Effects of finite volume on the K L − K S mass difference journal, June 2015

Lattice determination of the K → ( π π ) I = 2 decay amplitude A 2 journal, October 2012

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD journal, April 2018

Two particle states in an asymmetric box and the elastic scattering phases journal, July 2004

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

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

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

Erratum: Gluonic transversity from lattice QCD [Phys. Rev. D 94 , 014507 (2016)] journal, April 2017

Finite volume corrections to the two-particle decay of states with nonzero momentum journal, December 2005

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

Scattering processes and resonances from lattice QCD journal, April 2018

Finite volume matrix elements of two-body states conference, May 2019

Gluonic transversity from lattice QCD journal, July 2016

Elastic I = 3 / 2 p -wave nucleon-pion scattering amplitude and the Δ ( 1232 ) resonance from N f = 2 + 1 lattice QCD journal, January 2018

Electroweak matrix elements in the two-nucleon sector from lattice QCD journal, October 2004

An overview of XYZ new particles journal, May 2014

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

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

Excited meson radiative transitions from lattice QCD using variationally optimized operators journal, June 2015

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

First lattice QCD study of the gluonic structure of light nuclei journal, November 2017

Finite-volume effects due to spatially nonlocal operators journal, July 2018

Scalar mesons in a finite volume
journal, January 2011

Emerging Understanding of the $Δ I = 1 / 2$ Rule from Lattice QCD
journal, April 2013

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

Generalized Lüscher formula in multichannel baryon-meson scattering
journal, January 2013

On analytic properties of vertex parts in quantum field theory
journal, October 1959

Singularities in the physical region
journal, July 1965

Coupled-channel scattering on a torus
journal, July 2013

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

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

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

Discussion on triangle singularities in the $Λ_{b} \to J / ψ K^{-} p$ reaction
journal, October 2016

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

$K$ to $π π$ decay amplitudes from lattice QCD
journal, December 2011

Timelike pion form factor in lattice QCD
journal, March 2015

Proton-Proton Fusion and Tritium $β$ Decay from Lattice Quantum Chromodynamics
journal, August 2017

Double- $β$ decay matrix elements from lattice quantum chromodynamics
journal, September 2017

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

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

Relativistic, model-independent, multichannel $2 \to 2$ transition amplitudes in a finite volume
journal, July 2016

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

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

$π γ \to π π$ transition and the $ρ$ radiative decay width from lattice QCD
journal, October 2018

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

Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013

Heavy Physics Contributions to Neutrinoless Double Beta Decay from QCD
journal, October 2018

Parton Physics on a Euclidean Lattice
journal, June 2013

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

Lattice QCD and the Timelike Pion Form Factor
journal, August 2011

Heavy-quark QCD exotica
journal, March 2017

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

Two-baryon systems with twisted boundary conditions
journal, April 2014

Multichannel $1 \to 2$ transition amplitudes in a finite volume
journal, February 2015

$K \to (π π)_{I = 2}$ Decay Amplitude from Lattice QCD
journal, April 2012

Multichannel $0 \to 2$ and $1 \to 2$ transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015

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

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

Standard Model Prediction for Direct $C P$ Violation in $K \to π π$ Decay
journal, November 2015

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

Nuclear gluonometry
journal, June 1989

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

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

Hadronic molecules
journal, February 2018

Matrix elements of unstable states
journal, September 2012

Off-forward gluonic structure of vector mesons
journal, June 2017

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

Three-body unitarity in the finite volume
journal, December 2017

Effects of finite volume on the $K_{L} - K_{S}$ mass difference
journal, June 2015

Lattice determination of the $K \to (π π)_{I = 2}$ decay amplitude $A_{2}$
journal, October 2012

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD
journal, April 2018

Two particle states in an asymmetric box and the elastic scattering phases
journal, July 2004

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

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

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

Erratum: Gluonic transversity from lattice QCD [Phys. Rev. D 94 , 014507 (2016)]
journal, April 2017

Finite volume corrections to the two-particle decay of states with nonzero momentum
journal, December 2005

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

Scattering processes and resonances from lattice QCD
journal, April 2018

Finite volume matrix elements of two-body states
conference, May 2019

Gluonic transversity from lattice QCD
journal, July 2016

Elastic $I = 3 / 2$ $p$ -wave nucleon-pion scattering amplitude and the $Δ (1232)$ resonance from $N_{f} = 2 + 1$ lattice QCD
journal, January 2018

Electroweak matrix elements in the two-nucleon sector from lattice QCD
journal, October 2004

An overview of XYZ new particles
journal, May 2014

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

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

Excited meson radiative transitions from lattice QCD using variationally optimized operators
journal, June 2015

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

First lattice QCD study of the gluonic structure of light nuclei
journal, November 2017

Finite-volume effects due to spatially nonlocal operators
journal, July 2018

The hidden-charm pentaquark and tetraquark states
journal, June 2016

Issues and Opportunities in Exotic Hadrons
journal, April 2016

Finite-volume matrix elements in multiboson states
journal, April 2015