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

Hansen, Maxwell; Briceno, Raul

doi:10.1103/PhysRevD.92.074509

Title: Multichannel $0 \to 2$ and $1 \to 2$ transition amplitudes for arbitrary spin particles in a finite volume

Abstract

We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $$\textbf{0}\rightarrow\textbf{2}$$ and $$\textbf{1}\rightarrow\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\mathcal{J}~\rightarrow~(N\pi,N\eta,N\eta',\Sigma K,\Lambda K)$$ transitions, where $$\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.

Authors:

Hansen, Maxwell ^[1]; Briceno, Raul ^[2]

Univ. of Washington, Seattle, WA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Thu Oct 01 00:00:00 EDT 2015

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:: 1222198

Alternate Identifier(s):: OSTI ID: 1224363

Report Number(s):: JLAB-THY-15-2009; DOE/OR/23177-3291; arXiv:1502.04314
Journal ID: ISSN 1550-7998; PRVDAQ; TRN: US1600886

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

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

Additional Journal Information:: Journal Volume: 92; Journal Issue: 7; 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


                    Hansen, Maxwell, and Briceno, Raul. Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevD.92.074509.

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                    Hansen, Maxwell, & Briceno, Raul. Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume.  United States.  https://doi.org/10.1103/PhysRevD.92.074509

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                    Hansen, Maxwell, and Briceno, Raul. Thu .  
"Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume".  United States.  https://doi.org/10.1103/PhysRevD.92.074509.  https://www.osti.gov/servlets/purl/1222198.

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@article{osti_1222198,

  title        = {Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume},

  author       = {Hansen, Maxwell and Briceno, Raul},

  abstractNote = {We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $\textbf{0}\rightarrow\textbf{2}$ and $\textbf{1}\rightarrow\textbf{2}$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $N+\mathcal{J}~\rightarrow~(N\pi,N\eta,N\eta',\Sigma K,\Lambda K)$ transitions, where $\mathcal{J}$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.},

  doi          = {10.1103/PhysRevD.92.074509},

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

  number       = 7,

  volume       = 92,

  place        = {United States},

  year         = {Thu Oct 01 00:00:00 EDT 2015},

  month        = {Thu Oct 01 00:00:00 EDT 2015}

}

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Title: Multichannel 0→2 and 1→2 transition amplitudes for arbitrary spin particles in a finite volume

Abstract

Citation Formats

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Measurement of the Differential Branching Fraction and Forward-Backward Asymmetry for B → K ( * ) l + l − journal, October 2009

Measurements of the Angular Distributions in the Decays B → K ( * ) μ + μ − at CDF journal, February 2012

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Ab initio calculation of the neutron-proton mass difference journal, March 2015

QED corrections to hadronic processes in lattice QCD journal, April 2015

Two-particle elastic scattering in a finite volume including QED journal, October 2014

Lattice QCD calculation of nuclear parity violation journal, February 2012

Radiative Capture Reactions in Lattice Effective Field Theory journal, July 2013

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

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

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

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

Three particles in a finite volume journal, May 2012

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

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

The decay constant of the first excited pion from lattice QCD journal, November 2006

Decay constants of the pion and its excitations on the lattice journal, July 2014

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

Generalized Lüscher’s formula in multichannel baryon-baryon scattering journal, August 2014

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

Angular momentum on the lattice: The case of nonzero linear momentum journal, January 2006

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

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

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

Towards extracting the timelike pion form factor on CLS twoflavour ensembles journal, January 2018

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD journal, November 2017

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes journal, January 2018

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

Opportunities for Lattice QCD in quark and lepton flavor physics journal, November 2019

Hadrons and nuclei journal, November 2019

Lattice QCD and neutrino-nucleus scattering journal, November 2019

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations journal, October 2018

On the determination of Ω − Ω scattering amplitudes from finite volume spectra journal, December 2016

Isoscalar ππ Scattering and the σ Meson Resonance from QCD text, January 2017

Towards extracting the timelike pion form factor on CLS two-flavour ensembles text, January 2017

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

The role of the Euclidean signature in lattice calculations of quasi-distributions and other non-local matrix elements text, January 2017

Three-body Unitarity in the Finite Volume text, January 2017

Numerical study of the relativistic three-body quantization condition in the isotropic approximation text, January 2018

Scattering amplitudes from finite-volume spectral functions text, January 2019

Opportunities for lattice QCD in quark and lepton flavor physics text, January 2019

Lattice QCD and Neutrino-Nucleus Scattering text, January 2019

Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states text, January 2019

Title: Multichannel $0 \to 2$ and $1 \to 2$ transition amplitudes for arbitrary spin particles in a finite volume

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

Measurement of the Differential Branching Fraction and Forward-Backward Asymmetry for $B \to K^{(*)} l^{+} l^{-}$
journal, October 2009

Measurements of the Angular Distributions in the Decays $B \to K^{(*)} μ^{+} μ^{-}$ at CDF
journal, February 2012

Measurement of branching fractions and rate asymmetries in the rare decays $B \to K^{(*)} ℓ^{+} ℓ^{-}$
journal, August 2012

Differential branching fraction and angular analysis of the decay B 0 → K ∗0 μ + μ −
journal, August 2013

Measurement of Form-Factor-Independent Observables in the Decay $B^{0} \to K^{* 0} μ^{+} μ^{-}$
journal, November 2013

General analysis of $\bar{B} \to {\bar{K}}^{(*)} ℓ^{+} ℓ^{-}$ decays at low recoil
journal, February 2013

Understanding the $B \to K^{*} μ^{+} μ^{-}$ anomaly
journal, October 2013

$B \to K^{*}$ form factors from flavor data to QCD and back
journal, April 2014

Comprehensive Bayesian analysis of rare (semi)leptonic and radiative $$\varvec{B}$$ B decays
journal, June 2014

Lattice QCD calculation of form factors describing the rare decays $B \to K^{*} ℓ^{+} ℓ^{-}$ and $B_{s} \to ϕ ℓ^{+} ℓ^{-}$
journal, May 2014

Calculation of $B^{0} \to K^{* 0} μ^{+} μ^{-}$ and $B_{s}^{0} \to ϕ μ^{+} μ^{-}$ Observables Using Form Factors from Lattice QCD
journal, May 2014

$B_{s} \to K ℓ ν$ form factors from lattice QCD
journal, September 2014

Nuclear reactions from lattice QCD
journal, January 2015

Uncertainty quantification in lattice QCD calculations for nuclear physics
journal, February 2015

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

K→ππ decays in a finite volume
journal, December 2001

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

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

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

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

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

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

Matrix elements of unstable states
journal, September 2012

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

Electromagnetic Splittings and Light Quark Masses in Lattice QCD
journal, May 1996

QED in Finite Volume and Finite Size Scaling Effect on Electromagnetic Properties of Hadrons
journal, September 2008

Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei
journal, September 2014

Ab initio calculation of the neutron-proton mass difference
journal, March 2015

QED corrections to hadronic processes in lattice QCD
journal, April 2015

Two-particle elastic scattering in a finite volume including QED
journal, October 2014

Lattice QCD calculation of nuclear parity violation
journal, February 2012

Radiative Capture Reactions in Lattice Effective Field Theory
journal, July 2013

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

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

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

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

Three particles in a finite volume
journal, May 2012

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

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

The decay constant of the first excited pion from lattice QCD
journal, November 2006

Decay constants of the pion and its excitations on the lattice
journal, July 2014

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

Generalized Lüscher’s formula in multichannel baryon-baryon scattering
journal, August 2014

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

Angular momentum on the lattice: The case of nonzero linear momentum
journal, January 2006

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

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

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

Towards extracting the timelike pion form factor on CLS twoflavour ensembles
journal, January 2018

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes
journal, January 2018

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

Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019

Hadrons and nuclei
journal, November 2019

Lattice QCD and neutrino-nucleus scattering
journal, November 2019

Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations
journal, October 2018

On the determination of Ω − Ω scattering amplitudes from finite volume spectra
journal, December 2016

Isoscalar ππ Scattering and the σ Meson Resonance from QCD
text, January 2017

Towards extracting the timelike pion form factor on CLS two-flavour ensembles
text, January 2017

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

The role of the Euclidean signature in lattice calculations of quasi-distributions and other non-local matrix elements
text, January 2017

Three-body Unitarity in the Finite Volume
text, January 2017

Numerical study of the relativistic three-body quantization condition in the isotropic approximation
text, January 2018

Scattering amplitudes from finite-volume spectral functions
text, January 2019

Opportunities for lattice QCD in quark and lepton flavor physics
text, January 2019

Lattice QCD and Neutrino-Nucleus Scattering
text, January 2019

Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
text, January 2019