Double $\beta $ 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 longdistance deuteronpole contribution to the matrix element is separated from shorterdistance hadronic contributions. This polarizability, which is only accessible in doubleweak processes, cannot be constrained from single$$\beta$$ decay of nuclei, and is found to be smaller than the longdistance contributions in this calculation, but nonnegligible. 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 lightquark masses, are required for precise determinations of both twoneutrino and neutrinoless double$$\beta$$ decay rates in heavy nuclei.
 Authors:

 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:
 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):
 JLABTHY172500; DOE/OR/231774170; arXiv:1702.02929
Journal ID: ISSN 24700010; PRVDAQ; TRN: US1703218
 Grant/Contract Number:
 PHY1125915; PHY1515738; AC0205CH11231; AC0500OR22725; SC0010337; FG0200ER41132; SC0011090; FG0204ER41302; SC0010495; AC0506OR23177; SC0010337
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 24700010
 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. Doubleβ decay matrix elements from lattice quantum chromodynamics. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.054505.
Tiburzi, Brian C., Wagman, Michael L., Winter, Frank, Chang, Emmanuel, Davoudi, Zohreh, Detmold, William, Orginos, Kostas, Savage, Martin J., & Shanahan, Phiala E. Doubleβ decay matrix elements from lattice quantum chromodynamics. United States. doi:10.1103/PhysRevD.96.054505.
Tiburzi, Brian C., Wagman, Michael L., Winter, Frank, Chang, Emmanuel, Davoudi, Zohreh, Detmold, William, Orginos, Kostas, Savage, Martin J., and Shanahan, Phiala E. Mon .
"Doubleβ decay matrix elements from lattice quantum chromodynamics". United States. doi:10.1103/PhysRevD.96.054505. https://www.osti.gov/servlets/purl/1399867.
@article{osti_1399867,
title = {Doubleβ 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 longdistance deuteronpole contribution to the matrix element is separated from shorterdistance hadronic contributions. This polarizability, which is only accessible in doubleweak processes, cannot be constrained from single$\beta$ decay of nuclei, and is found to be smaller than the longdistance contributions in this calculation, but nonnegligible. 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 lightquark masses, are required for precise determinations of both twoneutrino 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}
}
Web of Science
Works referenced in this record:
Continuum limit and improved action in lattice theories
journal, September 1983
 Symanzik, K.
 Nuclear Physics B, Vol. 226, Issue 1
Axial polarizability and weak currents in nuclei
journal, November 1976
 Delorme, J.; Ericson, M.; Figureau, A.
 Annals of Physics, Vol. 102, Issue 1
Nucleonnucleon effective field theory without pions
journal, July 1999
 Chen, JiunnWei; Rupak, Gautam; Savage, Martin J.
 Nuclear Physics A, Vol. 653, Issue 4
Neutrinoless DoubleBeta Decay: a Brief Review
journal, April 2012
 Bilenky, S. M.; Giunti, C.
 Modern Physics Letters A, Vol. 27, Issue 13
Long distance contribution to the ${K}_{L}{K}_{S}$ mass difference
journal, July 2013
 Christ, N. H.; Izubuchi, T.; Sachrajda, C. T.
 Physical Review D, Vol. 88, Issue 1
Scalar densities and baryon mass differences in lattice QCD with Wilson fermions
journal, January 1987
 Maiani, L.; Martinelli, G.; Paciello, M. L.
 Nuclear Physics B, Vol. 293
Nonrenormalization Theorem for the StrangenessViolating Vector Currents
journal, August 1964
 Ademollo, M.; Gatto, R.
 Physical Review Letters, Vol. 13, Issue 7
Chiral TwoBody Currents in Nuclei: GamowTeller Transitions and Neutrinoless DoubleBeta Decay
journal, August 2011
 Menéndez, J.; Gazit, D.; Schwenk, A.
 Physical Review Letters, Vol. 107, Issue 6
Prospects for a lattice computation of rare kaon decay amplitudes: $K\to \pi {\ell}^{+}{\ell}^{}$ decays
journal, November 2015
 Christ, N. H.; Feng, X.; Portelli, A.
 Physical Review D, Vol. 92, Issue 9
Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double $\beta $ Decay Phenomenology
journal, August 2017
 Shanahan, Phiala E.; Tiburzi, Brian C.; Wagman, Michael L.
 Physical Review Letters, Vol. 119, Issue 6
Solving lattice QCD systems of equations using mixed precision solvers on GPUs
journal, September 2010
 Clark, M. A.; Babich, R.; Barros, K.
 Computer Physics Communications, Vol. 181, Issue 9
Double beta decay, Majorana neutrinos, and neutrino mass
journal, April 2008
 Avignone, Frank T.; Elliott, Steven R.; Engel, Jonathan
 Reviews of Modern Physics, Vol. 80, Issue 2
Neutrinodeuteron scattering in effective field theory at nexttonexttoleading order
journal, February 2001
 Butler, Malcolm; Chen, JiunnWei; Kong, Xinwei
 Physical Review C, Vol. 63, Issue 3
Precise halflife values for twoneutrino double $\beta $ decay
journal, March 2010
 Barabash, A. S.
 Physical Review C, Vol. 81, Issue 3
Hadronic vacuum polarization and muon $g2$ from magnetic susceptibilities on the lattice
journal, September 2015
 Bali, Gunnar S.; Endrődi, Gergely
 Physical Review D, Vol. 92, Issue 5
Moving multichannel systems in a finite volume with application to protonproton fusion
journal, November 2013
 Briceño, Raúl A.; Davoudi, Zohreh
 Physical Review D, Vol. 88, Issue 9
ProtonProton Fusion and Tritium $\beta $ Decay from Lattice Quantum Chromodynamics
journal, August 2017
 Savage, Martin J.; Shanahan, Phiala E.; Tiburzi, Brian C.
 Physical Review Letters, Vol. 119, Issue 6
Finitevolume electromagnetic corrections to the masses of mesons, baryons, and nuclei
journal, September 2014
 Davoudi, Zohreh; Savage, Martin J.
 Physical Review D, Vol. 90, Issue 5
Weak Transition Matrix Elements¶from FiniteVolume Correlation Functions
journal, May 2001
 Lellouch, Laurent; Lüscher, Martin
 Communications in Mathematical Physics, Vol. 219, Issue 1
Perturbative calculation of the electromagnetic form factors of the deuteron
journal, February 1999
 Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
 Physical Review C, Vol. 59, Issue 2
Status and future of nuclear matrix elements for neutrinoless doublebeta decay: a review
journal, March 2017
 Engel, Jonathan; Menéndez, Javier
 Reports on Progress in Physics, Vol. 80, Issue 4
Sea quark contributions to the electric polarizability of hadrons
journal, September 2014
 Freeman, Walter; Alexandru, Andrei; Lujan, Mike
 Physical Review D, Vol. 90, Issue 5
Relativistic, modelindependent, multichannel $2\to 2$ transition amplitudes in a finite volume
journal, July 2016
 Briceño, Raúl A.; Hansen, Maxwell T.
 Physical Review D, Vol. 94, Issue 1
Neutrinoless Double Beta Decay: 2015 Review
journal, January 2016
 Dell’Oro, Stefano; Marcocci, Simone; Viel, Matteo
 Advances in High Energy Physics, Vol. 2016
Twonucleon systems in a finite volume: Quantization conditions
journal, August 2013
 Briceño, Raúl; Davoudi, Zohreh; Luu, Thomas
 Physical Review D, Vol. 88, Issue 3
Nuclear $\sigma $ terms and scalarisoscalar WIMPnucleus interactions from lattice QCD
journal, April 2014
 Beane, S. R.; Cohen, S. D.; Detmold, W.
 Physical Review D, Vol. 89, Issue 7
Twoparticle elastic scattering in a finite volume including QED
journal, October 2014
 Beane, Silas R.; Savage, Martin J.
 Physical Review D, Vol. 90, Issue 7
Magnetic structure of light nuclei from lattice QCD
journal, December 2015
 Chang, Emmanuel; Detmold, William; Orginos, Kostas
 Physical Review D, Vol. 92, Issue 11
The proton and neutron magnetic moments in lattice QCD
journal, October 1982
 Martinelli, G.; Parisi, G.; Petronzio, R.
 Physics Letters B, Vol. 116, Issue 6
New calculations for phase space factors involved in double $\beta $ decay
journal, September 2013
 Stoica, Sabin; Mirea, Mihail
 Physical Review C, Vol. 88, Issue 3
Improved continuum limit lattice action for QCD with wilson fermions
journal, September 1985
 Sheikholeslami, B.; Wohlert, R.
 Nuclear Physics B, Vol. 259, Issue 4
Effective field theory of shortrange forces
journal, January 1999
 van Kolck, U.
 Nuclear Physics A, Vol. 645, Issue 2
Flavor singlet physics in lattice QCD with background fields
journal, March 2005
 Detmold, W.
 Physical Review D, Vol. 71, Issue 5
Magnetic polarizability of hadrons from lattice QCD in the background field method
journal, February 2006
 Lee, Frank X.; Zhou, Leming; Wilcox, Walter
 Physical Review D, Vol. 73, Issue 3
More effective field theory for nonrelativistic scattering
journal, June 1997
 Kaplan, David B.
 Nuclear Physics B, Vol. 494, Issue 12
Elastic and inelastic neutrino–deuteron scattering in effective field theory
journal, August 2000
 Butler, Malcolm; Chen, JiunnWei
 Nuclear Physics A, Vol. 675, Issue 34
Implementation of general background electromagnetic fields on a periodic hypercubic lattice
journal, October 2015
 Davoudi, Zohreh; Detmold, William
 Physical Review D, Vol. 92, Issue 7
Ab initio calculation of the neutronproton mass difference
journal, March 2015
 Borsanyi, S.; Durr, S.; Fodor, Z.
 Science, Vol. 347, Issue 6229
Pionic matrix elements in neutrinoless double $\beta $ decay
journal, April 1999
 Savage, Martin J.
 Physical Review C, Vol. 59, Issue 4
Nucleonnucleon scattering parameters in the limit of SU(3) flavor symmetry
journal, August 2013
 Beane, S. R.; Chang, E.; Cohen, S. D.
 Physical Review C, Vol. 88, Issue 2
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986
 Lüscher, M.
 Communications in Mathematical Physics, Vol. 105, Issue 2
Exploratory Lattice QCD Study of the Rare Kaon Decay ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$
journal, June 2017
 Bai, Ziyuan; Christ, Norman H.; Feng, Xu
 Physical Review Letters, Vol. 118, Issue 25
Protonproton fusion in effective field theory
journal, August 2001
 Kong, Xinwei; Ravndal, Finn
 Physical Review C, Vol. 64, Issue 4
A new expansion for nucleonnucleon interactions
journal, April 1998
 Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
 Physics Letters B, Vol. 424, Issue 34
Continuum limit and improved action in lattice theories
journal, September 1983
 Symanzik, K.
 Nuclear Physics B, Vol. 226, Issue 1
Neutrinoless double $\beta $ decay and effective field theory
journal, August 2003
 Prézeau, G.; RamseyMusolf, M.; Vogel, Petr
 Physical Review D, Vol. 68, Issue 3
Rearranging pionless effective field theory
journal, November 2001
 Beane, Silas R.; Savage, Martin J.
 Nuclear Physics A, Vol. 694, Issue 34
Onshell improved lattice gauge theories
journal, March 1985
 Lüscher, M.; Weisz, P.
 Communications in Mathematical Physics, Vol. 97, Issue 12
Effects of finite volume on the ${K}_{L}{K}_{S}$ mass difference
journal, June 2015
 Christ, N. H.; Feng, X.; Martinelli, G.
 Physical Review D, Vol. 91, Issue 11
First exploratory calculation of the longdistance contributions to the rare kaon decays $K\to \pi {\ell}^{+}{\ell}^{}$
journal, December 2016
 Christ, Norman H.; Feng, Xu; Jüttner, Andreas
 Physical Review D, Vol. 94, Issue 11
Octet baryon magnetic moments from lattice QCD: Approaching experiment from a threeflavor symmetric point
journal, June 2017
 Parreño, Assumpta; Savage, Martin J.; Tiburzi, Brian C.
 Physical Review D, Vol. 95, Issue 11
Disconnected contributions to the spin of the nucleon
journal, December 2015
 Chambers, A. J.; Horsley, R.; Nakamura, Y.
 Physical Review D, Vol. 92, Issue 11
First evaluation of in lattice QCD in the quenched approximation
journal, August 1982
 Fucito, F.; Parisi, G.; Petrarca, S.
 Physics Letters B, Vol. 115, Issue 2
Prospects for a lattice computation of rare kaon decay amplitudes. II. $K\to \pi \nu \overline{\nu}$ decays
journal, June 2016
 Christ, Norman H.; Feng, Xu; Portelli, Antonin
 Physical Review D, Vol. 93, Issue 11
Effective Field Theory for Lattice Nuclei
journal, February 2015
 Barnea, N.; Contessi, L.; Gazit, D.
 Physical Review Letters, Vol. 114, Issue 5
Electromagnetic and spin polarizabilities in lattice QCD
journal, June 2006
 Detmold, W.; Tiburzi, B. C.; WalkerLoud, A.
 Physical Review D, Vol. 73, Issue 11
A framework for the calculation of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchemainstance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/structbib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/structaff/dtd"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>N</mml:mi><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math> transition form factors on the lattice
journal, September 2014
 Agadjanov, Andria; Bernard, Véronique; Meißner, UlfG.
 Nuclear Physics B, Vol. 886
Neutrinoless double beta decay and chiral SU (3)
journal, June 2017
 Cirigliano, V.; Dekens, W.; Graesser, M.
 Physics Letters B, Vol. 769
Towards a perturbative theory of nuclear forces
journal, March 2002
 Beane, S. R.; Bedaque, P. F.; Savage, M. J.
 Nuclear Physics A, Vol. 700, Issue 12
On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements
journal, July 2017
 Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten
 Physical Review D, Vol. 96, Issue 1
Theory of neutrinos: a white paper
journal, October 2007
 Mohapatra, R. N.; Antusch, S.; Babu, K. S.
 Reports on Progress in Physics, Vol. 70, Issue 11
Twonucleon systems from effective field theory
journal, November 1998
 Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
 Nuclear Physics B, Vol. 534, Issue 12
Lattice QuantumChromodynamics Calculation of Some Baryon Magnetic Moments
journal, October 1982
 Bernard, Claude; Draper, Terrence; Olynyk, Kirk
 Physical Review Letters, Vol. 49, Issue 15
Two nucleons on a lattice
journal, April 2004
 Beane, S. R.; Bedaque, P. F.; Parreño, A.
 Physics Letters B, Vol. 585, Issue 12
Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry
journal, February 2013
 Beane, S. R.; Chang, E.; Cohen, S. D.
 Physical Review D, Vol. 87, Issue 3
FeynmanHellmann approach to the spin structure of hadrons
journal, July 2014
 Chambers, A. J.; Horsley, R.; Nakamura, Y.
 Physical Review D, Vol. 90, Issue 1
Twoparticle states on a torus and their relation to the scattering matrix
journal, May 1991
 Lüscher, Martin
 Nuclear Physics B, Vol. 354, Issue 23
Unitary Limit of TwoNucleon Interactions in Strong Magnetic Fields
journal, March 2016
 Detmold, William; Orginos, Kostas; Parreño, Assumpta
 Physical Review Letters, Vol. 116, Issue 11
Extracting electric polarizabilities from lattice QCD
journal, May 2009
 Detmold, W.; Tiburzi, B. C.; WalkerLoud, A.
 Physical Review D, Vol. 79, Issue 9
Extracting nucleon magnetic moments and electric polarizabilities from lattice QCD in background electric fields
journal, March 2010
 Detmold, W.; Tiburzi, B. C.; WalkerLoud, A.
 Physical Review D, Vol. 81, Issue 5
Phasespace factors for double $\beta $ decay
journal, March 2012
 Kotila, J.; Iachello, F.
 Physical Review C, Vol. 85, Issue 3
Up, down, and strange nucleon axial form factors from lattice QCD
journal, June 2017
 Green, Jeremy; Hasan, Nesreen; Meinel, Stefan
 Physical Review D, Vol. 95, Issue 11
Ab initio Calculation of the $np\to d\gamma $ Radiative Capture Process
journal, September 2015
 Beane, Silas R.; Chang, Emmanuel; Detmold, William
 Physical Review Letters, Vol. 115, Issue 13
Isovector charges of the nucleon from $2+1$ flavor QCD with clover fermions
journal, April 2017
 Yoon, Boram; Jang, YongChull; Gupta, Rajan
 Physical Review D, Vol. 95, Issue 7
Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics
journal, December 2014
 Beane, S. R.; Chang, E.; Cohen, S.
 Physical Review Letters, Vol. 113, Issue 25
The Chroma Software System for Lattice QCD
journal, March 2005
 Edwards, Robert G.; Joó, Bálint
 Nuclear Physics B  Proceedings Supplements, Vol. 140
Improving the convergence of NN effective field theory
journal, February 2000
 Phillips, Daniel R.; Rupak, Gautam; Savage, Martin J.
 Physics Letters B, Vol. 473, Issue 34
Works referencing / citing this record:
Value of the AxialVector Coupling Strength in β and ββ Decays: A Review
journal, November 2017
 Suhonen, Jouni T.
 Frontiers in Physics, Vol. 5
Value of the AxialVector Coupling Strength in β and ββ Decays: A Review
journal, November 2017
 Suhonen, Jouni T.
 Frontiers in Physics, Vol. 5