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

Briceno, Raul A.; Hansen, Maxwell T.

doi:10.1103/PhysRevD.94.013008

Title: Relativistic, model-independent, multichannel $2 \to 2$ transition amplitudes in a finite volume

Abstract

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $$\rho$$-meson form factor, in which the unstable nature of the $$\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.

Authors:

Briceno, Raul A. ^[1]; Hansen, Maxwell T. ^[2]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Johannes Gutenberg-Univ. Mainz, Mainz (Germany)

Publication Date:: Wed Jul 13 00:00:00 EDT 2016

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:: 1262312

Alternate Identifier(s):: OSTI ID: 1262447

Report Number(s):: JLAB-THY-15-2140; DOE/OR/23177-3556; arXiv:1509.08507
Journal ID: ISSN 2470-0010; PRVDAQ

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 94; Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite volume

Citation Formats


                    Briceno, Raul A., and Hansen, Maxwell T. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.94.013008.

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                    Briceno, Raul A., & Hansen, Maxwell T. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume.  United States.  https://doi.org/10.1103/PhysRevD.94.013008

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                    Briceno, Raul A., and Hansen, Maxwell T. Wed .  
"Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume".  United States.  https://doi.org/10.1103/PhysRevD.94.013008.  https://www.osti.gov/servlets/purl/1262312.

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@article{osti_1262312,

  title        = {Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume},

  author       = {Briceno, Raul A. and Hansen, Maxwell T.},

  abstractNote = {We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.},

  doi          = {10.1103/PhysRevD.94.013008},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 94,

  place        = {United States},

  year         = {Wed Jul 13 00:00:00 EDT 2016},

  month        = {Wed Jul 13 00:00:00 EDT 2016}

}

Copy to clipboard

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We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore »« less
Cited by 78
https://doi.org/10.1103/PhysRevD.92.074509

Full Text Available
$π π \to π γ^{*}$ amplitude and the resonant $ρ \to π γ^{*}$ transition from lattice QCD

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

We present a determination of themore »« less
https://doi.org/10.1103/PhysRevD.93.114508

Full Text Available
Constraining $1 + J \to 2$ coupled-channel amplitudes in a finite volume

Journal Article Briceño, Raúl A. ; Dudek, Jozef J. ; Leskovec, Luka - Physical Review D

Whether one is interested in accessing the excited spectrum of hadrons or testing the standard model of particle physics, electroweak transition processes involving multihadron channels in the final state play an important role in a variety of experiments. Presently the primary theoretical tool with which one can study such reactions is lattice QCD, which is defined in a finite spacetime volume. In this work, we investigate the feasibility of implementing existing finite-volume formalism in realistic lattice QCD calculation of reactions in which a stable hadron can transition to one of several two-hadron channels under the action of an external current.more »« less
https://doi.org/10.1103/PhysRevD.104.054509
$π γ \to π π$ transition and the $ρ$ radiative decay width from lattice QCD

Journal Article Alexandrou, Constantia ; Leskovec, Luka ; Meinel, Stefan ; ... - Physical Review. D.

In this paper, we report a lattice QCD determination of the πγ → ππ transition amplitude for the P-wave, I = 1 two-pion final state, as a function of the photon virtuality and ππ invariant mass. The calculation was performed with 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV, on a 32³ × 96 lattice with L ≈ 3.6 fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all ππ momenta up to |more »« less
Cited by 30
https://doi.org/10.1103/PhysRevD.98.074502
Long-distance contributions to neutrinoless double beta decay $π^{-} \to π^{+} e e$

Journal Article Tuo, Xin-Yu ; Feng, Xu ; Jin, Lu-Chang - Physical Review D

Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, thenmore »« less
Cited by 18
https://doi.org/10.1103/PhysRevD.100.094511

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Title: Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume

Abstract

Citation Formats

Scalar mesons in a finite volume journal, January 2011

Parity violation in proton-proton scattering at 13.6 MeV journal, February 1991

Connecting physical resonant amplitudes and lattice QCD journal, June 2016

On the Recovery and Resolution of Exponential Relaxation Rates from Experimental Data: A Singular-Value Analysis of the Laplace Transform Inversion in the Presence of Noise journal, September 1982

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

Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass journal, October 2014

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

Measurement of parity-violating γ -ray asymmetry in the capture of polarized cold neutrons on protons journal, January 2011

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

Hadronic parity violation journal, July 2013

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

Search for parity violation in neutron-proton capture journal, March 1977

Observation of 1.5% Parity-Nonconserving γ -Ray Asymmetry journal, June 1971

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

Parity nonconservation in polarized-neutron transmission through La 139 journal, November 1991

Timelike pion form factor in lattice QCD journal, March 2015

Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD journal, July 2006

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

Measurement of Parity Nonconservation in pp Scattering at 45 MeV journal, March 1980

Experimental Test of Parity Conservation in Beta Decay journal, February 1957

Parity Violation in Proton-Proton Scattering at 221 MeV journal, December 2001

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

Nucleon to Δ and Δ form factors in lattice QCD conference, January 2012

Two-nucleon systems in a finite volume: Quantization conditions journal, August 2013

Predicting positive parity B s mesons from lattice QCD journal, November 2015

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

Three particles in a finite volume journal, May 2012

Precision measurement of parity nonconservation in proton-proton scattering at 45 MeV journal, April 1987

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

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

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

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

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

The anapole form factor of the deuteron journal, April 2001

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

Parity-violating polarization in np → d γ with a pionless effective field theory journal, May 2010

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

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

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

A new experimental study of the circular polarization of np capture γ-rays journal, April 1984

Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry journal, August 2013

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

Parity violation in proton-proton scattering at 221 MeV journal, September 2003

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

Matrix elements of unstable states journal, September 2012

D s mesons with D K and D * K scattering near threshold journal, August 2014

Parity-Violating Asymmetry of the 501-keV Gamma Ray Emitted in the Decay of Hf 180 m journal, November 1971

Two nucleon systems at m π ∼ 450 MeV from lattice QCD journal, December 2015

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

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

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

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

Reanalysis of lattice QCD spectra leading to the D s0 ∗ (2317) and D s1 ∗ (2460) journal, May 2015

The theory of parity violation in few-nucleon systems journal, September 2013

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

Parity-violating neutron spin rotation in hydrogen and deuterium journal, January 2012

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

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

Parity in Nuclear Reactions journal, August 1957

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

Parity violation in proton-proton scattering at 45 MeV journal, November 1984

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

ρ meson decay in 2 + 1 flavor lattice QCD journal, November 2011

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

Two parity-violating asymmetries from in pionless effective field theories journal, November 2010

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

An effective-field-theory analysis of low-energy parity-violation in nucleon–nucleon scattering journal, May 2009

Two-nucleon systems in a finite volume. II. S 1 3 − D 1 3 coupled channels and the deuteron journal, December 2013

Ab initio Calculation of the n p → d γ Radiative Capture Process journal, September 2015

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

Possible Interference Phenomena between Parity Doublets journal, November 1956

Δ ( 1232 ) Axial Charge and Form Factors from Lattice QCD journal, September 2011

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

Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics journal, December 2014

Lattice QCD calculation of nuclear parity violation journal, February 2012

Title: Relativistic, model-independent, multichannel $2 \to 2$ transition amplitudes in a finite volume

Scalar mesons in a finite volume
journal, January 2011

Parity violation in proton-proton scattering at 13.6 MeV
journal, February 1991

Connecting physical resonant amplitudes and lattice QCD
journal, June 2016

On the Recovery and Resolution of Exponential Relaxation Rates from Experimental Data: A Singular-Value Analysis of the Laplace Transform Inversion in the Presence of Noise
journal, September 1982

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

Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
journal, October 2014

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

Measurement of parity-violating $γ$ -ray asymmetry in the capture of polarized cold neutrons on protons
journal, January 2011

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

Hadronic parity violation
journal, July 2013

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

Search for parity violation in neutron-proton capture
journal, March 1977

Observation of 1.5% Parity-Nonconserving $γ$ -Ray Asymmetry
journal, June 1971

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

Parity nonconservation in polarized-neutron transmission through ${}^{139}{La}$
journal, November 1991

Timelike pion form factor in lattice QCD
journal, March 2015

Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD
journal, July 2006

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

Measurement of Parity Nonconservation in $pp$ Scattering at 45 MeV
journal, March 1980

Experimental Test of Parity Conservation in Beta Decay
journal, February 1957

Parity Violation in Proton-Proton Scattering at 221 MeV
journal, December 2001

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

Nucleon to Δ and Δ form factors in lattice QCD
conference, January 2012

Two-nucleon systems in a finite volume: Quantization conditions
journal, August 2013

Predicting positive parity $B_{s}$ mesons from lattice QCD
journal, November 2015

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

Three particles in a finite volume
journal, May 2012

Precision measurement of parity nonconservation in proton-proton scattering at 45 MeV
journal, April 1987

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

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

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

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

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

The anapole form factor of the deuteron
journal, April 2001

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

Parity-violating polarization in $np \to d γ$ with a pionless effective field theory
journal, May 2010

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

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

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

A new experimental study of the circular polarization of np capture γ-rays
journal, April 1984

Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry
journal, August 2013

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

Parity violation in proton-proton scattering at 221 MeV
journal, September 2003

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

Matrix elements of unstable states
journal, September 2012

$D_{s}$ mesons with $D K$ and $D * K$ scattering near threshold
journal, August 2014

Parity-Violating Asymmetry of the 501-keV Gamma Ray Emitted in the Decay of ${}^{180 m}{Hf}$
journal, November 1971

Two nucleon systems at $m_{π} \sim 450 MeV$ from lattice QCD
journal, December 2015

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

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

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

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

Reanalysis of lattice QCD spectra leading to the D s0 ∗ (2317) and D s1 ∗ (2460)
journal, May 2015

The theory of parity violation in few-nucleon systems
journal, September 2013

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

Parity-violating neutron spin rotation in hydrogen and deuterium
journal, January 2012

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

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

Parity in Nuclear Reactions
journal, August 1957

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

Parity violation in proton-proton scattering at 45 MeV
journal, November 1984

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

$ρ$ meson decay in $2 + 1$ flavor lattice QCD
journal, November 2011

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

Two parity-violating asymmetries from in pionless effective field theories
journal, November 2010

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

An effective-field-theory analysis of low-energy parity-violation in nucleon–nucleon scattering
journal, May 2009

Two-nucleon systems in a finite volume. II. ${}^{3}S_{1} − {}^{3}D_{1}$ coupled channels and the deuteron
journal, December 2013

Ab initio Calculation of the $n p \to d γ$ Radiative Capture Process
journal, September 2015

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

Possible Interference Phenomena between Parity Doublets
journal, November 1956

$Δ (1232)$ Axial Charge and Form Factors from Lattice QCD
journal, September 2011

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

Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics
journal, December 2014

Lattice QCD calculation of nuclear parity violation
journal, February 2012

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

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