Double-β decay matrix elements from lattice quantum chromodynamics

Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.

doi:10.1103/PhysRevD.96.054505

Title: Double- $β$ decay matrix elements from lattice quantum chromodynamics

Abstract

A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the $$nn\to ppee\overline{\nu}_e\overline{\nu}_e$$ transition is described in detail, expanding on the results presented in Ref. [1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-$$\beta$$ decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-$$\beta$$ decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-$$\beta$$ decay rates in heavy nuclei.

Authors:

Tiburzi, Brian C. ^[1]; Wagman, Michael L. ^[2]; Winter, Frank ^[3]; Chang, Emmanuel ^[4]; Davoudi, Zohreh ^[5]; Detmold, William ^[5]; Orginos, Kostas ^[6]; Savage, Martin J. ^[4]; Shanahan, Phiala E. ^[5]

City Univ. (CUNY), NY (United States). Dept. of Physics, Graduate School and University Center
Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory, Dept. of Physics
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
College of William and Mary, Williamsburg, VA (United States). Dept. of Physics

Publication Date:: 2017-09-11

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: NPLQCD Collaboration

OSTI Identifier:: 1399867

Alternate Identifier(s):: OSTI ID: 1389119

Report Number(s):: JLAB-THY-17-2500; DOE/OR/-23177-4170; arXiv:1702.02929
Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1703218

Grant/Contract Number:: PHY11-25915; PHY15-15738; AC02-05CH11231; AC05-00OR22725; SC00-10337; FG02-00ER41132; SC0011090; FG02-04ER41302; SC0010495; AC05-06OR23177; SC0010337

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Tiburzi, Brian C., Wagman, Michael L., Winter, Frank, Chang, Emmanuel, Davoudi, Zohreh, Detmold, William, Orginos, Kostas, Savage, Martin J., and Shanahan, Phiala E. Double-β decay matrix elements from lattice quantum chromodynamics.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevD.96.054505.

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                    Tiburzi, Brian C., Wagman, Michael L., Winter, Frank, Chang, Emmanuel, Davoudi, Zohreh, Detmold, William, Orginos, Kostas, Savage, Martin J., & Shanahan, Phiala E. Double-β decay matrix elements from lattice quantum chromodynamics.  United States.  https://doi.org/10.1103/PhysRevD.96.054505

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                    Tiburzi, Brian C., Wagman, Michael L., Winter, Frank, Chang, Emmanuel, Davoudi, Zohreh, Detmold, William, Orginos, Kostas, Savage, Martin J., and Shanahan, Phiala E. Mon .  
"Double-β decay matrix elements from lattice quantum chromodynamics".  United States.  https://doi.org/10.1103/PhysRevD.96.054505.  https://www.osti.gov/servlets/purl/1399867.

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@article{osti_1399867,

  title        = {Double-β decay matrix elements from lattice quantum chromodynamics},

  author       = {Tiburzi, Brian C. and Wagman, Michael L. and Winter, Frank and Chang, Emmanuel and Davoudi, Zohreh and Detmold, William and Orginos, Kostas and Savage, Martin J. and Shanahan, Phiala E.},

  abstractNote = {A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the $nn\to ppee\overline{\nu}_e\overline{\nu}_e$ transition is described in detail, expanding on the results presented in Ref. [1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-$\beta$ decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-$\beta$ decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-$\beta$ decay rates in heavy nuclei.},

  doi          = {10.1103/PhysRevD.96.054505},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 96,

  place        = {United States},

  year         = {2017},

  month        = {9}

}

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Title: Double- β decay matrix elements from lattice quantum chromodynamics

Abstract

Citation Formats

Continuum limit and improved action in lattice theories journal, September 1983

Axial polarizability and weak currents in nuclei journal, November 1976

Nucleon-nucleon effective field theory without pions journal, July 1999

Neutrinoless Double-Beta Decay: a Brief Review journal, April 2012

Long distance contribution to the K L − K S mass difference journal, July 2013

Scalar densities and baryon mass differences in lattice QCD with Wilson fermions journal, January 1987

Nonrenormalization Theorem for the Strangeness-Violating Vector Currents journal, August 1964

Chiral Two-Body Currents in Nuclei: Gamow-Teller Transitions and Neutrinoless Double-Beta Decay journal, August 2011

Prospects for a lattice computation of rare kaon decay amplitudes: K → π ℓ + ℓ − decays journal, November 2015

Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double- β Decay Phenomenology journal, August 2017

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

Double beta decay, Majorana neutrinos, and neutrino mass journal, April 2008

Neutrino-deuteron scattering in effective field theory at next-to-next-to-leading order journal, February 2001

Precise half-life values for two-neutrino double- β decay journal, March 2010

Hadronic vacuum polarization and muon g − 2 from magnetic susceptibilities on the lattice journal, September 2015

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

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

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

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

Perturbative calculation of the electromagnetic form factors of the deuteron journal, February 1999

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review journal, March 2017

Sea quark contributions to the electric polarizability of hadrons journal, September 2014

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

Neutrinoless Double Beta Decay: 2015 Review journal, January 2016

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

Nuclear σ terms and scalar-isoscalar WIMP-nucleus interactions from lattice QCD journal, April 2014

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

Magnetic structure of light nuclei from lattice QCD journal, December 2015

The proton and neutron magnetic moments in lattice QCD journal, October 1982

New calculations for phase space factors involved in double- β decay journal, September 2013

Improved continuum limit lattice action for QCD with wilson fermions journal, September 1985

Effective field theory of short-range forces journal, January 1999

Flavor singlet physics in lattice QCD with background fields journal, March 2005

Magnetic polarizability of hadrons from lattice QCD in the background field method journal, February 2006

More effective field theory for non-relativistic scattering journal, June 1997

Elastic and inelastic neutrino–deuteron scattering in effective field theory journal, August 2000

Implementation of general background electromagnetic fields on a periodic hypercubic lattice journal, October 2015

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

Pionic matrix elements in neutrinoless double- β decay journal, April 1999

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

Exploratory Lattice QCD Study of the Rare Kaon Decay K + → π + ν ν ¯ journal, June 2017

Proton-proton fusion in effective field theory journal, August 2001

A new expansion for nucleon-nucleon interactions journal, April 1998

Continuum limit and improved action in lattice theories journal, September 1983

Neutrinoless double β decay and effective field theory journal, August 2003

Rearranging pionless effective field theory journal, November 2001

On-shell improved lattice gauge theories journal, March 1985

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

First exploratory calculation of the long-distance contributions to the rare kaon decays K → π ℓ + ℓ − journal, December 2016

Octet baryon magnetic moments from lattice QCD: Approaching experiment from a three-flavor symmetric point journal, June 2017

Disconnected contributions to the spin of the nucleon journal, December 2015

First evaluation of in lattice QCD in the quenched approximation journal, August 1982

Prospects for a lattice computation of rare kaon decay amplitudes. II. K → π ν ν ¯ decays journal, June 2016

Effective Field Theory for Lattice Nuclei journal, February 2015

Electromagnetic and spin polarizabilities in lattice QCD journal, June 2006

Neutrinoless double beta decay and chiral SU (3) journal, June 2017

Towards a perturbative theory of nuclear forces journal, March 2002

On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements journal, July 2017

Theory of neutrinos: a white paper journal, October 2007

Two-nucleon systems from effective field theory journal, November 1998

Lattice Quantum-Chromodynamics Calculation of Some Baryon Magnetic Moments journal, October 1982

Two nucleons on a lattice journal, April 2004

Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry journal, February 2013

Feynman-Hellmann approach to the spin structure of hadrons journal, July 2014

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

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields journal, March 2016

Extracting electric polarizabilities from lattice QCD journal, May 2009

Extracting nucleon magnetic moments and electric polarizabilities from lattice QCD in background electric fields journal, March 2010

Phase-space factors for double- β decay journal, March 2012

Up, down, and strange nucleon axial form factors from lattice QCD journal, June 2017

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

Isovector charges of the nucleon from 2 + 1 -flavor QCD with clover fermions journal, April 2017

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

The Chroma Software System for Lattice QCD journal, March 2005

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Title: Double- $β$ decay matrix elements from lattice quantum chromodynamics

Continuum limit and improved action in lattice theories
journal, September 1983

Axial polarizability and weak currents in nuclei
journal, November 1976

Nucleon-nucleon effective field theory without pions
journal, July 1999

Neutrinoless Double-Beta Decay: a Brief Review
journal, April 2012

Long distance contribution to the $K_{L} - K_{S}$ mass difference
journal, July 2013

Scalar densities and baryon mass differences in lattice QCD with Wilson fermions
journal, January 1987

Nonrenormalization Theorem for the Strangeness-Violating Vector Currents
journal, August 1964

Chiral Two-Body Currents in Nuclei: Gamow-Teller Transitions and Neutrinoless Double-Beta Decay
journal, August 2011

Prospects for a lattice computation of rare kaon decay amplitudes: $K \to π ℓ^{+} ℓ^{-}$ decays
journal, November 2015

Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double- $β$ Decay Phenomenology
journal, August 2017

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

Double beta decay, Majorana neutrinos, and neutrino mass
journal, April 2008

Neutrino-deuteron scattering in effective field theory at next-to-next-to-leading order
journal, February 2001

Precise half-life values for two-neutrino double- $β$ decay
journal, March 2010

Hadronic vacuum polarization and muon $g - 2$ from magnetic susceptibilities on the lattice
journal, September 2015

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

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

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

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

Perturbative calculation of the electromagnetic form factors of the deuteron
journal, February 1999

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review
journal, March 2017

Sea quark contributions to the electric polarizability of hadrons
journal, September 2014

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

Neutrinoless Double Beta Decay: 2015 Review
journal, January 2016

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

Nuclear $σ$ terms and scalar-isoscalar WIMP-nucleus interactions from lattice QCD
journal, April 2014

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

Magnetic structure of light nuclei from lattice QCD
journal, December 2015

The proton and neutron magnetic moments in lattice QCD
journal, October 1982

New calculations for phase space factors involved in double- $β$ decay
journal, September 2013

Improved continuum limit lattice action for QCD with wilson fermions
journal, September 1985

Effective field theory of short-range forces
journal, January 1999

Flavor singlet physics in lattice QCD with background fields
journal, March 2005

Magnetic polarizability of hadrons from lattice QCD in the background field method
journal, February 2006

More effective field theory for non-relativistic scattering
journal, June 1997

Elastic and inelastic neutrino–deuteron scattering in effective field theory
journal, August 2000

Implementation of general background electromagnetic fields on a periodic hypercubic lattice
journal, October 2015

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

Pionic matrix elements in neutrinoless double- $β$ decay
journal, April 1999

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

Exploratory Lattice QCD Study of the Rare Kaon Decay $K^{+} \to π^{+} ν \bar{ν}$
journal, June 2017

Proton-proton fusion in effective field theory
journal, August 2001

A new expansion for nucleon-nucleon interactions
journal, April 1998

Continuum limit and improved action in lattice theories
journal, September 1983

Neutrinoless double $β$ decay and effective field theory
journal, August 2003

Rearranging pionless effective field theory
journal, November 2001

On-shell improved lattice gauge theories
journal, March 1985

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

First exploratory calculation of the long-distance contributions to the rare kaon decays $K \to π ℓ^{+} ℓ^{-}$
journal, December 2016

Octet baryon magnetic moments from lattice QCD: Approaching experiment from a three-flavor symmetric point
journal, June 2017

Disconnected contributions to the spin of the nucleon
journal, December 2015

First evaluation of in lattice QCD in the quenched approximation
journal, August 1982

Prospects for a lattice computation of rare kaon decay amplitudes. II. $K \to π ν \bar{ν}$ decays
journal, June 2016

Effective Field Theory for Lattice Nuclei
journal, February 2015

Electromagnetic and spin polarizabilities in lattice QCD
journal, June 2006

Neutrinoless double beta decay and chiral SU (3)
journal, June 2017

Towards a perturbative theory of nuclear forces
journal, March 2002

On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements
journal, July 2017

Theory of neutrinos: a white paper
journal, October 2007

Two-nucleon systems from effective field theory
journal, November 1998

Lattice Quantum-Chromodynamics Calculation of Some Baryon Magnetic Moments
journal, October 1982

Two nucleons on a lattice
journal, April 2004

Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry
journal, February 2013

Feynman-Hellmann approach to the spin structure of hadrons
journal, July 2014

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

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields
journal, March 2016

Extracting electric polarizabilities from lattice QCD
journal, May 2009

Extracting nucleon magnetic moments and electric polarizabilities from lattice QCD in background electric fields
journal, March 2010

Phase-space factors for double- $β$ decay
journal, March 2012

Up, down, and strange nucleon axial form factors from lattice QCD
journal, June 2017

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

Isovector charges of the nucleon from $2 + 1$ -flavor QCD with clover fermions
journal, April 2017

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

The Chroma Software System for Lattice QCD
journal, March 2005

Improving the convergence of NN effective field theory
journal, February 2000

Nucleon axial radius and muonic hydrogen—a new analysis and review
journal, July 2018

Hyperons: the strange ingredients of the nuclear equation of state
journal, September 2018

Oracles for Gauss's law on digital quantum computers
journal, April 2019