Prospects for γ ⋆ γ ⋆ → π π via lattice QCD

Briceño, Raúl A.; Jackura, Andrew W.; Rodas, Arkaitz; Guerrero, Juan V.

doi:10.1103/PhysRevD.107.034504

Title: Prospects for $γ^{⋆} γ^{⋆} \to π π$ via lattice QCD

Abstract

The $$\gamma^\star \gamma^\star \to \pi \pi$$ scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where $$3\pi$$ states can go on shell, and is exact up to exponentially small corrections that scale like $$\mathcal{O}(e^{-m_\pi L})$$, where $$L$$ is the spatial extent of the cubic volume and $$m_\pi$$ is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain $$\pi \pi \to \pi\pi$$, $$\pi \gamma^\star \to \pi$$, $$\gamma^\star \to\pi\pi$$, and $$\pi\pi\gamma^\star \to\pi\pi$$ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations.

Authors:

;

; Rodas, Arkaitz; Guerrero, Juan V.

Publication Date:: Mon Feb 13 00:00:00 EST 2023

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1924379

Alternate Identifier(s):: OSTI ID: 1959169

Report Number(s):: JLAB-THY-22-3727; DOE/OR/23177-5624
Journal ID: ISSN 2470-0010; PRVDAQ; 034504

Grant/Contract Number:: AC05-06OR23177; SC0019229; SC0018416; LD2117

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 107 Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; form factors; lattice QCD; particle interactions; quantum electrodynamics; quantum field theory

Citation Formats


                    Briceño, Raúl A., Jackura, Andrew W., Rodas, Arkaitz, and Guerrero, Juan V. Prospects for γ ⋆ γ ⋆ → π π via lattice QCD.  United States: N. p., 2023. 
Web.  doi:10.1103/PhysRevD.107.034504.

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                    Briceño, Raúl A., Jackura, Andrew W., Rodas, Arkaitz, & Guerrero, Juan V. Prospects for γ ⋆ γ ⋆ → π π via lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.107.034504

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                    Briceño, Raúl A., Jackura, Andrew W., Rodas, Arkaitz, and Guerrero, Juan V. Mon .  
"Prospects for γ ⋆ γ ⋆ → π π via lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.107.034504.

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@article{osti_1924379,

  title        = {Prospects for γ ⋆ γ ⋆ → π π via lattice QCD},

  author       = {Briceño, Raúl A. and Jackura, Andrew W. and Rodas, Arkaitz and Guerrero, Juan V.},

  abstractNote = {The $\gamma^\star \gamma^\star \to \pi \pi$ scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where $3\pi$ states can go on shell, and is exact up to exponentially small corrections that scale like $\mathcal{O}(e^{-m_\pi L})$, where $L$ is the spatial extent of the cubic volume and $m_\pi$ is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain $\pi \pi \to \pi\pi$, $\pi \gamma^\star \to \pi$, $\gamma^\star \to\pi\pi$, and $\pi\pi\gamma^\star \to\pi\pi$ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations.},

  doi          = {10.1103/PhysRevD.107.034504},

  journal      = {Physical Review. D.},

  number       = 3,

  volume       = 107,

  place        = {United States},

  year         = {Mon Feb 13 00:00:00 EST 2023},

  month        = {Mon Feb 13 00:00:00 EST 2023}

}

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Title: Prospects for γ ⋆ γ ⋆ → π π via lattice QCD

Abstract

Citation Formats

Two-Photon Decays of Charmonia from Lattice QCD journal, October 2006

Towards a data-driven analysis of hadronic light-by-light scattering journal, November 2014

f0(1370) Controversy from Dispersive Meson-Meson Scattering Data Analyses journal, February 2023

Dispersion relation for hadronic light-by-light scattering: two-pion contributions journal, April 2017

Glueball spectrum from an anisotropic lattice study journal, July 1999

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

Timelike pion form factor in lattice QCD journal, March 2015

Global parameterization of $$\pi \pi $$ππ scattering up to 2 $${\mathrm {\,GeV}}$$GeV journal, December 2019

Dispersive analysis of the γγ⁎ → ππ process journal, February 2019

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

Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon journal, June 2017

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

Energy-Dependent π + π + π + Scattering Amplitude from QCD journal, January 2021

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

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

Constraining 1 + J → 2 coupled-channel amplitudes in a finite volume journal, September 2021

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm journal, April 2021

Glueball spectrum and matrix elements on anisotropic lattices journal, January 2006

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

Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon journal, September 2018

b 1 resonance in coupled π ω , π ϕ scattering from lattice QCD journal, September 2019

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

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

Lattice calculation of the pion transition form factor π 0 → γ * γ * journal, October 2016

Identification of a Scalar Glueball journal, December 2008

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

Two-pion contribution to hadronic vacuum polarization journal, February 2019

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

P -wave nucleon-pion scattering amplitude in the Δ ( 1232 ) channel from lattice QCD journal, May 2021

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

Consistency checks for two-body finite-volume matrix elements. II. Perturbative systems journal, May 2020

Extraction of low-energy constants of single- and double- β decays from lattice QCD: A sensitivity analysis journal, May 2022

I = 3 Three-Pion Scattering Amplitude from Lattice QCD journal, January 2020

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

The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions journal, November 2020

Three-Body Dynamics of the a 1 ( 1260 ) Resonance from Lattice QCD journal, November 2021

Evidence for a scalar glueball journal, June 1995

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

Location, Correlation, Radiation: Where is the σ, what is its Structure, and what is its Coupling to Photons? journal, June 2007

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

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD journal, April 2020

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

Anomalous magnetic moment of the muon in a dispersive approach journal, December 2014

The hadronic light-by-light contribution to the muon’s anomalous magnetic moment journal, July 2019

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

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

Scattering processes and resonances from lattice QCD journal, April 2018

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

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

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

Comprehensive amplitude analysis of γ γ → π + π − , π 0 π 0 and K ¯ K below 1.5 GeV journal, August 2014

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

Hadronic light-by-light contribution to $$(g-2)_\mu $$ from lattice QCD with SU(3) flavor symmetry journal, September 2020

The status of glueballs journal, February 2013

Scalar mesons in a finite volume journal, January 2011

I = 1 / 2 S -wave and P -wave K π scattering and the κ and K * resonances from lattice QCD journal, December 2020

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

Two-neutrino double- β decay in pionless effective field theory from a Euclidean finite-volume correlation function journal, December 2020

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Is f 0 ( 1710 ) a glueball? journal, December 2014

Dispersive approach to hadronic light-by-light scattering journal, September 2014

Scalar quarkonium masses and mixing with the lightest scalar glueball journal, December 1999

Have We Seen Our First Glueball? journal, April 1981

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

Hadronic light-by-light scattering in the muon g − 2 journal, January 2019

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

Two-current transition amplitudes with two-body final states journal, June 2022

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Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions journal, January 2020

Title: Prospects for $γ^{⋆} γ^{⋆} \to π π$ via lattice QCD

Two-Photon Decays of Charmonia from Lattice QCD
journal, October 2006

Towards a data-driven analysis of hadronic light-by-light scattering
journal, November 2014

f0(1370) Controversy from Dispersive Meson-Meson Scattering Data Analyses
journal, February 2023

Dispersion relation for hadronic light-by-light scattering: two-pion contributions
journal, April 2017

Glueball spectrum from an anisotropic lattice study
journal, July 1999

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

Timelike pion form factor in lattice QCD
journal, March 2015

Global parameterization of $$\pi \pi $$ππ scattering up to 2 $${\mathrm {\,GeV}}$$GeV
journal, December 2019

Dispersive analysis of the γγ⁎ → ππ process
journal, February 2019

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

Rescattering Effects in the Hadronic-Light-by-Light Contribution to the Anomalous Magnetic Moment of the Muon
journal, June 2017

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

Energy-Dependent $π^{+} π^{+} π^{+}$ Scattering Amplitude from QCD
journal, January 2021

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

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

Constraining $1 + J \to 2$ coupled-channel amplitudes in a finite volume
journal, September 2021

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
journal, April 2021

Glueball spectrum and matrix elements on anisotropic lattices
journal, January 2006

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

Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon
journal, September 2018

$b_{1}$ resonance in coupled $π ω$ , $π ϕ$ scattering from lattice QCD
journal, September 2019

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

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

Lattice calculation of the pion transition form factor $π^{0} \to γ^{} γ^{}$
journal, October 2016

Identification of a Scalar Glueball
journal, December 2008

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

Two-pion contribution to hadronic vacuum polarization
journal, February 2019

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

$P$ -wave nucleon-pion scattering amplitude in the $Δ (1232)$ channel from lattice QCD
journal, May 2021

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

Consistency checks for two-body finite-volume matrix elements. II. Perturbative systems
journal, May 2020

Extraction of low-energy constants of single- and double- β decays from lattice QCD: A sensitivity analysis
journal, May 2022

$I = 3$ Three-Pion Scattering Amplitude from Lattice QCD
journal, January 2020

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

The glueball spectrum of SU(3) gauge theory in 3 + 1 dimensions
journal, November 2020

Three-Body Dynamics of the $a_{1} (1260)$ Resonance from Lattice QCD
journal, November 2021

Evidence for a scalar glueball
journal, June 1995

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

Location, Correlation, Radiation: Where is the σ, what is its Structure, and what is its Coupling to Photons?
journal, June 2007

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

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD
journal, April 2020

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

Anomalous magnetic moment of the muon in a dispersive approach
journal, December 2014

The hadronic light-by-light contribution to the muon’s anomalous magnetic moment
journal, July 2019

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

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

Scattering processes and resonances from lattice QCD
journal, April 2018

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

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

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

Comprehensive amplitude analysis of $γ γ \to π^{+} π^{-}, π^{0} π^{0}$ and $\bar{K} K$ below 1.5 GeV
journal, August 2014

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

Hadronic light-by-light contribution to $$(g-2)_\mu $$ from lattice QCD with SU(3) flavor symmetry
journal, September 2020

The status of glueballs
journal, February 2013

Scalar mesons in a finite volume
journal, January 2011

$I = 1 / 2$ $S$ -wave and $P$ -wave $K π$ scattering and the $κ$ and $K^{*}$ resonances from lattice QCD
journal, December 2020

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

Two-neutrino double- $β$ decay in pionless effective field theory from a Euclidean finite-volume correlation function
journal, December 2020

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

Theoretical analysis of the $γ γ \to π^{0} η$ process
journal, December 2017

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

Is $f_{0} (1710)$ a glueball?
journal, December 2014

Dispersive approach to hadronic light-by-light scattering
journal, September 2014

Scalar quarkonium masses and mixing with the lightest scalar glueball
journal, December 1999

Have We Seen Our First Glueball?
journal, April 1981

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

Hadronic light-by-light scattering in the muon g − 2
journal, January 2019

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

Two-current transition amplitudes with two-body final states
journal, June 2022

On-shell representations of two-body transition amplitudes: Single external current
journal, June 2021

The γπ → ππ anomaly from lattice QCD and dispersion relations
journal, December 2021

Implementing the three-particle quantization condition for π+π+K+ and related systems
journal, February 2022

Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
journal, January 2020

A comprehensive lattice study of SU(3) glueballs
journal, July 1993

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